Information-minimizing stationary financial market dynamics

Authors: Eckhard Platen

Abstract

The paper derives the dynamics of a financial market from basic mathematical principles. It models the market dynamics using independent stationary scalar diffusions, assumes the existence of its growth optimal portfolio (GOP), interprets the market as a communication system, and minimizes, in an information-theoretical sense, the joint information of the risk-neutral pricing measure with respect to the real-world probability measure. In this information-minimizing market, its basic independent securities, their sums, minimum variance portfolio, and GOP, as well as the GOP of the entire market, represent squared radial Ornstein-Uhlenbeck processes with additivity and self-similarity properties.

Complexity vs Empirical Score

Math Complexity: 8.5/10
Empirical Rigor: 2.5/10
Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated, first-principles mathematical derivation of financial market dynamics using information theory, stochastic differential equations, and Lie-group symmetries. However, it is entirely theoretical with minimal empirical testing or data validation, leaving backtesting and practical implementation to future research.

Research Flowchart

  flowchart TD
    A[Goal: Derive market dynamics from basic mathematical & info-theory principles] --> B[Inputs: Independent stationary scalar diffusions & existence of GOP]
    B --> C[Method: Model market as a communication system]
    C --> D[Compute: Minimize joint info of risk-neutral measure vs real-world measure]
    D --> E[Outcome: Securities, portfolios & GOP form squared radial Ornstein-Uhlenbeck processes]
    E --> F[Key Properties: Additivity & self-similarity in multi-asset dynamics]

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Monetary policy and a stock market boom-bust cycle (2005)
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Keynasian chaos (1986)
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Convergence of Discretized Stochastic (Interest Rate) Processes with Stochastic Drift Term (1998)
Equity-linked policies (1986)
Coherent risk measures on general probability spaces (2002)
Exponential hedging and entropic penalties (2002)
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Numerical method for some \sdes with multiplicative noise (2005)
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Some properties of the W ishart processes and a matrix extension of the Hartman-Watson laws (2004)
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Stochastic Processes (1953)
Measure Theory (1994)
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Liens entre 'equations diff'erentielles stochastiques et ordinaires (1977)
On the term structure of interest rates (1978)
A random volatility correction for the B lack- S choles option pricing formula (1987)
Prices in Financial Markets (1990)
Numerical methods for forward-backward stochastic differential equations (1996)
Mixing, Properties and Examples (1994)
The functional central limit theorem for strongly mixing processes (1994)
The stochastic method for numerical simulations: H igher order corrections (1983)
Scalar diffusion in simulated helical turbulence with molecular diffusivity (1984)
Numerical integration of stochastic differential equations with variable diffusivity (1986)
Computer simulation of multiplicative stochastic differential equations (1991)
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The GARCH option pricing model (1995)
Augmented GARCH (p,q) process and its diffusion limit (1996)
Security Markets - Stochastic Models (1988)
Dynamic Asset Pricing Theory (2001)
First-to-default valuation (1998)
Affine Processes and Applications in Finance (2003)
Risk and Valuation of Collateralized Debt Obligations (2001)
Efficient M onte C arlo simulation of security prices (1995)
Multiperiod security markets with differential information; martingales and resolution times (1986)
Multi-factor term structure models (1994)
A yield-factor model of interest rates (1996)
An overview of V alue at R isk (1997)
Analytic V alue at R isk with jumps and credit risk (2001)
Transform analysis and option pricing for affine jump diffusions (2000)
Mean-variance hedging in continuous time (1991)
Recursive valuation of defaultable securities and the timing of resolution of uncertainty (1995)
Simulated moments estimation of M arkov models of asset prices (1993)
Credit Risk : Pricing, Measurement, and Management (2003)
An exact solution to a dynamic portfolio choice problem under transaction costs (1991)
Implied volatility functions: E mpirical tests (1998)
Arbitrage pricing with stochastic volatility (1992)
Model Art (1993)
Pricing with a smile (1994)
Stabilizing non-fundamental asset price movements under discretion and limited information (2005)
Importance sampling for sums of random variables with heavy tails (2007)
Stochastic differential equations and turbulent dispersion (1983)
About a M onte- C arlo algorithm for the solution of the S chr"odinger equation (1968)
Bond and bond option pricing based on the current term structure (1989)
Long forward and zero-coupon rates can never fall (1996)
Markov Processes, Vol. I and Vol. II (1965)
Life expectancy in industrial and developing countries in 2023 (2024)
Influence of noise on D uffing- V an der P ol oscillators (1986)
Applications of generalized L 'evy motions in finance (2002)
Hyperbolic distributions in finance (1995)
New Insights into Smile, Mispricing, and Value at Risk: T he Hyperbolic Model* (1998)
Optimal replication of options with transaction costs and trading restictions (1993)
Optimal monetary policy in a liquidity trap (2003)
Approximate methods for calculating path integrals (1985)
Invariant probabilities for systems in a random environment - with applications to the B russelator (1983)
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On the movement of small particles suspended in stationary liquid demanded by molecular-kinetic theory of heat (1905)
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Bubbles, convexity and the B lack- S choles equation (2009)
Numerical method for some nonlinear stochastic differential equations (2005)
The microstructural foundations of leverage effect and rough volatility (2018)
Likelihood inference for discretely observed non-linear diffusions (2001)
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Multi-factor models of the term structure of interest rates (1992)
A pricing formula for options on coupon bonds (1989)
Computations of G reeks in a market with jumps via the M alliavin calculus (2004)
Further results on the constant elasticity of variance call option pricing model (1982)
The multiple stochastic integral (1982)
Optimal derivative design under dynamic risk measures (2004)
Stochastic Calculus and Applications (1982)
Hidden Markov Models: Estimation and Control (1995)
Hidden M arkov filtering for a mean reverting interest rate model (1999)
Approximations to solutions of the Z akai filtering equation (1989)
An application of hidden M arkov models to asset allocation problems (1997)
A general fractional white noise theory and applications to finance (2003)
Pricing claims on non tradable assets (2004)
Binomial Models in Finance (2006)
On models of default risk (2000)
A short proof of a martingale representation result (1988)
Mathematics of Financial Markets (2005)
Filtering derivative security valuations from market prices (1997)
Hidden M arkov chain filtering for generalised B essel processes (2001)
Modelling Extremal Events. For Insurance and Finance (1997)
Correlation: P itfalls and alternatives (1999)
Correlation and Dependencies in Risk Management: P roperties and Pitfalls (2002)
Stochastic Calculus in Manifolds (1989)
Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. \ Inflation (1982)
Modelling the persistence of conditional variances. W ith comments and a reply by the authors (1986)
Measuring and Testing the Impact of News on Volatility (1993)
Linear congruential generators for parallel M onte C arlo: the leap-frog case (1998)
MCMC analysis of diffusion models with application to finance (2001)
The impact of jumps in equity index volatility and returns (2003)
Die Monte Carlo-Methode und verwandte Fragen (1975)
Statistical Modeling (1982)
Random processes for solving classical equations of mathematical physics (1984)
Partial Differential Equations (1999)
Asian options revisited: I nverting the L aplace transformation (1995)
Some fundamentals of electricity derivatives (1998)
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Approximation von stochastischen D ifferenzialgleichungen auf D igital- und H ybridrechnern (1976)
Zur S imulation stetiger stochastischer W irtschaftsmodelle (1976)
Mandelbrot and the stable P aretian hypothesis (1963)
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Some Properties of Symmetric Stable Distributions (1968)
Parameter Estimates for Symmetric Stable Distributions (1971)
Long-term growth in a short-term market (1974)
Symmetric Multivariate and Related Distributions (1990)
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Fractals, Physics of Solids and Liquids (1988)
Two singular diffusion problems (1951)
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An Introduction to Probability Theory and Its Applications (1971)
Numerical solution of stochastic differential equations (1990)
Second order methods for solving stochastic differential equations (1992)
Stochastic Portfolio Theory (2002)
Relative Arbitrage in Volatility-Stabilized Markets
Quantum Mechanics and Path-Integrals (1965)
Options arbitrage in imperfect markets (1989)
A general characterization of one factor affine term structure models (2001)
Time-Inhomogeneous Affine Processes (2005)
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Applications of the balanced method to stochastic differential equations in filtering (1999)
Risk minimizing hedging strategies under partial observation (1999)
Monte Carlo: Concepts, Algorithms and Applications (1996)
Predicting stock market volatility: a new measure (1995)
Optimal long term growth rate of expected utility of wealth (1999)
Controlled Markov Processes and Viscosity Solutions (1992)
Stochastic optimal control, international finance and debt (2004)
Positive Interest (1996)
Computational Techniques for Fluid Dynamics (1988)
Convergence of numerical schemes for stochastic differential equations (2001)
Central limit theorem for a recurrent diffusion process and the Markov chain obtained by discretization (1984)
Approximate discrete-time schemes for statistics of diffusion processes (1989)
On estimating the diffusion coefficient from discrete observations (1993)
A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting (1984)
Calcul d’ I t� sans probabilit�s (1981)
Probabilistic aspects of options (1991)
Quantile hedging (1999)
Efficient hedging: C ost versus shortfall risk (2000)
Quadratic variation and an extension of I t^o’s formula (1995)
Hedging of Contingent Claims under Incomplete Information (1991)
A microeconomic approach to diffusion models for stock prices (1993)
Stochastic Finance. An Introduction In Discrete Time (2002)
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Fixed-income volatility management (1991)
Interest rate volatility as a stochastic factor (1991)
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Approximation of a conditional W iener integral (1968)
Financial modelling in a fast mean-reverting stochastic volatility environment (1999)
Derivatives in Markets with Stochastic Volatility (2000)
Variance reduction for M onte C arlo simulation in a stochastic volatility environment (2002)
Monte C arlo methods for stochastic volatility models (1997)
Small noise expansion and importance sampling (1997)
Applications of M alliavin calculus to M onte C arlo methods in finance (1999)
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Second-order algorithm for the numerical integration of colored-noise problems (1991)
Financial Market and Monetary Policy (1995)
Portfolio selection: T the effects of uncertain means, variances and covariances (1971)
Difference methods for stochastic ordinary differential equations (1965)
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Expected stock returns and volatility (1987)
Derivative asset analysis in models with level-dependent and stochastic volatility. M athematics of F inance, P art II (1997)
Risk minimizing hedging strategies under restricted information: T he case of stochastic volatility models observable only at random discrete times (1999)
A nonlinear filtering approach to volatility estimation with a view towards high frequency data (2001)
Partial Differential Equations of Parabolic Type (1968)
Stochastic Differential Equations and Applications, Vol. I (1975)
Stochastic Differential Equations and Applications, Vol. II (1976)
Economic implications of extraordinary movements in stock prices (1989)
Short-run fluctuations in foreign exchange rates: E vidence from the data 1973-1979 (1982)
Simulation of stochastic processes (1987)
Quantification of spread risk by means of historical simulation (2002)
Almost sure characterization of martingales (1994)
An empitical Bayes approach to efficient portfolio selection (1986)
For better performance: constrain portfolio weights (1988)
Pricing of financial derivatives via simulation (1995)
Stochastic differential equations for the non-linear filtering problem (1972)
A generalization of C lark’s formula (1977)
Empirical analysis of implied volatility: S tocks, Bonds and Currencies (1991)
Business Cycle Theory (1987)
The algebra of iterated stochastic integrals (1994)
Diversification - A multi-facetted concept (2013)
A basis for iterated stochastic integrals (1995)
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Variable step size control in the numerical solution of stochastic differential equations (1997)
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Handbook of Stochastic Methods. For Physics, Chemistry and the Natural Sciences (1983)
The order of Approximations for Solutions of I t^ o -Type Stochastic Differential Equations with Jumps (2004)
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The Volatility Surface. A Practitioner’s Guide (2006)
Consistent modeling of SPX and VIX options (2008)
Volatility is rough (2018)
Numerical Initial Value Problems in Ordinary Differential Equations (1971)
$ L ^p$- W asserstein- M etriken und A pproximation stochastischer D ifferentialgleichungen (1989)
Simultaneous time and chance discretization for stochastic differential equations (1995)
Discretization for stochastic differential equations, $ L ^p$ W asserstein metrics, and econometrical models (1996)
The computation of continuous integrals by the M onte C arlo method (1958)
Changes of numeraire, changes of probability measures and pricing of options (1995)
Diffusions for global optimization (1986)
Asset prices are B rownian motion: O nly in business time (2001)
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Limit theorems for discretely observed stochastic volatility models (1997)
Parameter estimation for discretely observed stochastic volatility models (1998)
Stochastic volatility models as hidden M arkov models and statistical applications (2000)
Random Number Generation and Monte Carlo Methods (1998)
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An Introduction to Mathematical Risk Theory (1979)
Life Insurance Mathematics (1997)
On the probability and severity of ruin (1987)
Option pricing by E sscher transforms (1994)
The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin (1997)
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The A merican put options valued analytically (1984)
Valuation by approximation: A comparison of alternative option valuation techniques (1985)
Turbulent Cascades in Foreign Exchange Markets. (1996)
Stochastic Volatility (1996)
On applications of the It^o - T aylor expansions to finance: H edging and V alue-at- R isk problems (2001)
Incorporating Event Risk into V alue at R isk (2001)
Stochastic convenience yield and the pricing of oil contingent claims (1990)
Stochastic Differential Equations (1972)
Stochastic Differential Equations and their Applications (1982)
The Theory of Stochastic Processes (1979)
Improved multi-level Monte Carlo convergence using Milstein scheme (2007)
Multi-level M onte C arlo path simulation (2008)
Smoking adjoints: Fast Monte Carlo Greeks (2006)
Analysing multi-level M onte C arlo for options with non-globally L ipschitz payoff (2009)
Exact stochastic simulation of coupled chemical reactions (1977)
Approximate accelerated stochastic simulation of chemically reacting systems (2001)
The effects of transactions costs and different borrowing and lending rates on the option pricing model: A note (1984)
"Uber die Stabilit"at des Euler-Schemas f"ur eine Affine Stochastische Differentialgleichung mit Ged"achtnis (2001)
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Monte Carlo Methods in Financial Engineering (2004)
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Numerical solution of jump-diffusion LIBOR market models (2003)
Convergence of a Discretization Scheme for Jump-Diffusion Processes with State-Dependent Intensities (2003)
Arbitrage-free discretization of lognormal forward LIBOR and swap rate models (2000)
A Canonical Representation for the Noncentral W ishart Distribution Useful for Simulation (1976)
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Importance sampling for stochastic simulations (1989)
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Weak approximation of killed diffusion (2000)
Computation of G reeks for barrier and look-back options using M alliavin calculus (2003)
A regression-based M onte- C arlo method to solve backward stochastic differential equations (2005)
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A survey and some generalizations of B essel processes (2003)
Estimating the early exercise boundary and pricing A merican options (1994)
Mean reversion interest rate modeling (1992)
Valuation of two-factor term structure models (1995)
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Mean-square rates of convergence in the continuous time simulation annealing algorithm in $ \cal R ^d$ (1988)
Lognormality of rates and term structure models (1994)
Stochastic averaging principle for systems with pathwise uniqueness (1995)
Averaging E uler-type difference schemes (1997)
Euler-type approximation for systems of stochastic differential equations (1989)
Averaging principle and systems of singularly perturbed stochastic differential equations (1990)
On an approximation method for a class of stochastic singularly perturbed systems (1993)
Optimal portfolios for logarithmic utility (2000)
A complete explicit solution to the log-optimal portfolio problem (2003)
Digital Communications with Space Applications (1964)
Shift Register Sequences (1967)
A filtering approach to pricing in multifactor term structure models (2001)
A filtered no arbitrage model for term structures from noisy data (2005)
On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies (1825)
High–frequency data in financial markets: I ssues and applications (1997)
A variance reduction technique for use with the extrapolated E uler method for numerical solution of stochastic differential equations (1994)
The nonlinear accelerator and the persistance of business cycles (1951)
Rate of convergence of an approximate solution of stochastic differential equations (1980)
ARCH Models and Financial Applications (1997)
Indirect inference (1993)
Derivative Pricing with Multivariate Stochastic Volatility: A pplication to Credit Risk (2004)
Stochastic switching in absorptive optical bistability (1981)
Aspects of Risk Theory (1991)
Minimizing transaction costs of option hedging strategies (1996)
Path-dependent options: E xtending the M onte C arlo simulation approach (1997)
The 4/2 stochastic volatility model (2017)
Strong solutions and quantization-based numerical schemes for a class of non-Markovian volatility models — → 2503.00243
Solvable affine term structure models (2008)
Maximum entropy principle with general deviation measures (2009)
Approximation of stochastic differential equations with modified fractional B rownian motion (1998)
A parabolic \sde with fractional B rownian motion input (1999)
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Numerical integration of stochastic differential equations (1987)
On weak convergence of semimartingales (1981)
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An Introduction to Probability and Statistics using BASIC (1979)
Insider trading in a continuous time market model (1998)
Approximation of L yapunov exponents of stochastic differential systems on compact manifolds (1990)
Approximation of L yapunov exponents of nonlinear stochastic differential equations (1996)
Impossibility of informationally efficient markets (1980)
Optimal investment strategies for controlling drawdowns. (1993)
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Valuing futures and options on volatility (1996)
Higher order numerical schemes for affinely controlled nonlinear systems (2001)
Pathwise approximation of random ordinary differential equations (2001)
Higher order numerical approximation of switching systems (2006)
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Asymptotic dynamics and VaR of large diversified portfolios in a jump-diffusion market (2004)
Step control in numerical solution of stochastic differential equations (2003)
The Practice of Risk Management (1998)
On the mollifier approximation for solutions of stochastic differential equations (1982)
Approximation theorems based on random partitions for stochastic differential equations and applications (1984)
Small and large time implied volatility under the minimal market model (2009)
Asymptotic inference for a linear stochastic differential equation with time delay (1999)
Euler scheme and tempered distributions (2006)
Volatility is (mostly) path-dependent (2023)
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A note on E uler’s approximations (1998)
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Managing Smile Risk (2002)
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Semiparametric Diffusion Estimation and Application to a Stock Market Model (2008)
Xplo R e: An Interactive Statistical Computing Environment (1995)
Investment Guarantees: The New Science of Modeling and Risk Management for Equity-Linked Life Insurance (2003)
Simulation of nonlinear stochastic equations with applications in modelling water pollution (1976)
Modelling, simulation and control of stochastic systems with application in wastewater treatment (1977)
Simulation of multivariate nonlinear stochastic systems (1979)
Approximate integration of a class of stochastic differential equations (1985)
Martingale and arbitrage in multiperiod securities markets (1979)
Martingales and stochastic integrals in the theory of continuous trading (1981)
A stochastic calculus model of continuous trading: C omplete markets (1983)
Stochastic Stability of Differential Equations (1980)
A M onte- C arlo method with inherited parallelism for solving partial differential equations with boundary conditions (1999)
A numerical scheme using excursion theory for simulating stochastic differential equations with reflection and local time at a boundary (2000)
A numerical scheme using It^o excursion for simulating local time resp. stochastic differential equations with reflection (1999)
M onte- C arlo simulation of killed diffusion (2000)
A numerical scheme using excursion theory for simulating \sdes with reflection and local time at a boundary (2000)
Weak Approximation of Stochastic Partial Differential Equations (2003)
A Numerical Approximation of Parabolic Stochastic Differential Equations driven by a P oisson Random Measure (2006)
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Gamma: Exploring Euler’s Constant (2003)
A second-order M onte- C arlo method for the solution of the I to stochastic differential equation (1986)
Roots of the transcendental equation associated with a certain differential equation (1950)
Convergence from discrete to continuous time contingent claims prices (1990)
Valuation of derivative securities using stochastic analytic and numerical methods (1995)
Modelling the stochastic dynamics of volatility for equity indices (2001)
Bond pricing and the term structure of interest rates: A new methodology for contingent claim valuation (1992)
Valuation of A merican bond options for a two-factor interest rate term structure model (1995)
Option pricing and hedging under stochastic and past dependent volatility (1992)
American style option pricing in a two-factor truncated G aussian interest rate model (1996)
European style option pricing in a two-factor truncated G aussian interest rate model (1996)
Pricing in a truncated G aussian interest rate model (1996)
Valuation of FX barrier options under stochastic volatility (1996)
Option valuation under stochastic volatility using the K arhunen- L oeve expansion (1997)
European pricing and hedging for an alternative market model (1999)
Pricing and hedging of index options for an alternative market model (2000)
A variance reduction technique based on integral representations (2002)
Consistent pricing and hedging for a modified constant elasticity of variance model (2002)
Pricing and hedging of index derivatives under an alternative asset price model with endogenous stochastic volatility (2002)
Perfect hedging of index derivatives under a minimal market model (2002)
Pricing of index options under a minimal market model with lognormal scaling (2003)
A minimal market model with random initial scaling (2005)
A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets (2001)
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Computational studies in continuous time nonlinear filtering (1988)
Sistemi dinamici stocastici (1989)
$ A $-stability of implicit R unge- K utta methods for systems with additive noise (1992)
Convergence and stability of implicit R unge- K utta methods for systems with multiplicative noise (1993)
Bessel Functions of Matrix Argument (1955)
A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
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A risky asset model with strong dependence through fractal activity time (1999)
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Analysis of the term structure of implied volatilities (1994)
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Brownian Motion (1980)
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Mean-square and asymptotic stability of numerical methods for stochastic ordinary differential equations (2000)
An algorithmic introduction to numerical simulation of stochastic differential equations (2001)
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation (2004)
MAPLE and MATLAB for stochastic differential equations in finance (2002)
Numerical methods for nonlinear stochastic differential equations with jumps (2005)
Convergence and Stability of Implicit Methods for Jump-Diffusion Systems (2006)
Strong convergence rates for backward E uler on a class of nonlinear jump-diffusion problems (2007)
Convergence of M onte C arlo simulations involving the mean-reverting square root process (2005)
Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations (2007)
Strong convergence of E uler-type methods for nonlinear stochastic differential equations (2002)
Real world volatility modeling (2009)
Portfolio management and transaction costs (1993)
Hedging General Claims (1993)
On the time of a diffusion process spends along a line (1993)
Term structure movements and pricing of interest rate claims (1986)
Models of endogenous stochastic volatility (1994)
Optimal delta hedging under transaction costs (1993)
Optimal replication of contingent claims under transaction costs (1989)
Binomial Methods in Finance (2006)
A comparison with L eland’s result on transaction costs (1997)
Pricing and hedging in the presence of transaction costs under local risk minimisation (1999)
Numerical Methods for Engineers and Scientists (1993)
Beitr"age zur schwachen A pproximation stochastischer D ifferentialgleichungen (1994)
Stability of weak numerical schemes for stochastic differential equations (1995)
On quasi- M onte C arlo simulation of stochastic differential equations (1997)
Optimal approximation of stochastic differential equations by adaptive step-size control (2000)
Step-size control for the uniform approximation of systems of \sdes with additive noise (2000)
The optimal discretization of stochastic differential equations (2001)
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Stability of superimplicit numerical methods for stochastic differential equations (1996)
Approximating large diversified portfolios (2000)
Option pricing under incompleteness and stochastic volatility (1992)
The lognormal interest rate model and E urodollar futures (1993)
Hedging option portfolios in the presence of transaction costs (1993)
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Options, Futures, and Other Derivative Securities (1993)
Options, Futures and Other Derivatives (2000)
The pricing of options on assets with stochastic volatilities (1987)
The use of control variate techniques in option pricing (1988)
Pricing interest rate derivative securities (1990)
Efficient procedures for valuing E uropean and A merican path-dependent options (1993)
The economic plausibility of strict local martingales in financial modelling (2010)
Benchmarking and Fair Pricing Applied to Two Market Models (2005)
A formula for interchanging normalized sums and I t^o integrals (2006)
Hedging for the long run (2008)
Hedging for the long run (2012)
A Visual Classification of local martingales (2008)
A Visual Criterion for Identifying I t^o Diffusions as Martingales or Strict Local Martingales (2009)
Weak tail conditions for local martingales (2012)
M$^6$ - O n minimal market models and minimal martingale measures (2010)
Getting the drift (2001)
Fair pricing using deflators and decrement copulas: T he unit linked endowment approach (2004)
On the Stochastic Dynamics of Stock Market Volatility (1997)
Intrinsic market time: A n interpretation of global market volatility (1997)
The marginal distributions of returns and volatility (1997)
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Subordinated market index models: A comparison (1997)
Option pricing for a logstable asset price model (1999)
Measuring risk in V alue-at- R isk based on S tudent’s t-distribution (1999)
Quasi-likelihood estimation for semimartingales (1986)
Simulation and Inference for Stochastic Differential Equations With R Examples (2008)
Industry classification benchmark (2008)
Modeling co-movements and tail dependency in the international stock market via copulae (2009)
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Optimal stopping and the A merican put (1991)
Monte Carlo Methods in Finance (2002)
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Asymptotic error distribution for the E uler method for stochastic differential equations (1998)
Limit Theorems for Stochastic Processes (2003)
Variational inequalities and the pricing of A merican options (1990)
Pricing equity-linked pure endowments with risky assets that follow L evy processes (2005)
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Approximation of stochastic differential equations driven by $\alpha$-stable L 'evy motion (1996)
Simulation and Chaotic Behavior of $\alpha$-stable Stochastic Processes (1994)
Efficient numerical solution of stochastic differential equations using exponential timestepping (2000)
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Option Pricing (1983)
Coherent risk measures and good-deal bounds (2001)
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The F eynman- K ac formula and decomposition of B rownian paths (1996)
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Grossissements de filtrations: exemples et applications (1985)
Binomial models for the term structure of interest (2000)
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Approximating processes of stochastic diffusion models under spatial uncertainty (2005)
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Likelihood-based Inference in Cointegrated Vector Autoregressive Models (1995)
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Options on the maximum or the minimum of several assets (1987)
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Arbitrage and viability in security markets with fixed trading costs (2001)
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Large financial markets: A symptotic arbitrage and contiguity (1994)
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Balanced M ilstein Methods for Ordinary SDE s (2006)
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Convergence to fractional B rownian motion and to the telecom process: T he integral representation approach (2008)
Theory of Economic Dynamics (1952)
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Optimal portfolios for exponential L'evy processes (2000)
New results in linear filtering and prediction theory (1961)
Monte Carlo Methods in Quantum Problems (1984)
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Monte C arlo G reeks for financial products via approximative transition densities (2008)
Multinomial approximating models for options with $k$ state variables (1991)
The rate of convergence in M aruyama’s invariance principle (1985)
Optimal portfolio choice with parameter uncertainty (2007)
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The rate of convergence for approximate solutions of stochastic differential equations (1989)
Error estimation for the E uler- M aruyama approximate solutions of stochastic differential equations (1995)
Convergence rates for the E uler- M aruyama type approximate solutions of stochastic differential equations (1996)
Confidence intervals of discretized E uler- M aruyama approximate solutions of SDE s (1997)
Strong approximation of reflecting B rownian motion using penalty method and its application to computer simulation (2000)
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Nonlinear filtering of an interactive multiple model with small observation noise: N umerical methods (1998)
Pathwise solutions of stochastic differential equations (1981)
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Optimization problems in the theory of continuous trading (1989)
Portfolio Theory and Arbitrage (2021)
The numeraire portfolio in semimartingale financial models (2007)
Explicit solution of a general consumption/investment problem (1986)
Existence and uniqueness of multi-agent equilibrium in a stochastic dynamic consumption/investment model (1990)
Brownian Motion and Stochastic Calculus (1991)
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Martingale and duality methods for utility maximization in an incomplete market (1991)
Bayesian adaptive portfolio optimization (2001)
On financial markets where only buy-and-hold trading is possible (2008)
Minimizing the expected market time to reach a certain wealth level (2010)
The num' e raire property and long-term growth optimality for drawdown-constrained investments (2017)
Multiplicative approximation of wealth processes involving no-short-sale strategies via simple trading (2008)
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A Second Course in Stochastic Processes (1981)
A Theory of Trading Volume (1986)
The Relation between Price Changes and Trading Volume: A Survey (1987)
Weather risk swap valuation (2003)
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Consistent ML estimator for drift parameters of both ergodic and nonergodic diffusions (1989)
Australian Stock Market Volatility: 1875-1987 (1993)
Statistical R omberg extrapolation: A new variance reduction method and applications to option pricing (2005)
An optimal control variance reduction method for density estimation (2008)
Efficient portfolios in the asset liability context (1995)
Distribution theory of spherical distributions and a locationscale parameter generalization (1970)
A new interpretation of information rate (1956)
An assessment of Black-Scholes hedging of index options (1999)
A pricing method for options on average asset values (1990)
The diffusion of E uclidean shape. (1989)
Computer algebra and stochastic analysis: S ome possibilities (1990)
Doing stochastic calculus with M athematica (1993)
The term structure of interest rates as a G aussian random field (1994)
Some probabilistic properties of Bessel functions (1978)
The pricing of FX barrier options (1992)
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Estimation of an ergodic diffusion from discrete observations (1997)
Estimating equations based on eigenfunctions for a discretely observed diffusion process (1999)
A generalization of the mutual fund theorem (1999)
The analytic valuation of A merican options (1990)
Numerical methods for \sdes with P oisson white shot noise (2007)
A simplified approach to the valuation of A merican options and applications (1993)
Theoretical Aspects of Population Genetics (1971)
Diffusion approximation in past dependent models and applications to option pricing (1991)
Efficient hedging and pricing life insurance policies in a jump-diffusion model (2005)
Efficient hedging when asset prices follow a geometric P oisson process with unknown intensities (2004)
Criticality and Phase Transition in Stock-Price Fluctuations (2006)
Numerical integration of multiplicative-noise stochastic differential equations (1985)
Spectrum of certain non-self-adjoint operators and solutions of L angevin equations with complex drift (1985)
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Statistical Techniques in Simulation. Part II (1975)
The effect of estimation risk on optimal portfolio choice (1976)
The interaction of guarantees, surplus distribution and asset allocation in with-profit life insurance policies (2007)
The Systematic Derivation of Higher Order Numerical Schemes for Stochastic Differential Equations (2002)
Pathwise convergent higher order numerical schemes for random ordinary differential equations (2007)
The pathwise convergence of approximation schemes for stochastic differential equations (2007)
The numerical solution of stochastic differential equations (1977)
A survey of numerical methods for stochastic differential equations (1989)
Relations between multiple I to and S tratonovich integrals (1991)
Stratonovich and I to stochastic T aylor expansions (1991)
Higher order implicit strong numerical schemes for stochastic differential equations (1992)
Numerical methods for stochastic differential equations (1995)
Stochastic differential equations: A pplications and numerical methods (1992)
Extrapolation methods for the weak approximation of I to diffusions (1995)
Stochastic T aylor expansions and higher order numerical schemes for stochastic differential equations (1991)
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Effective simulation of optimal trajectories in stochastic control (1992)
Higher order approximate M arkov chain filters (1993)
Numerical Solution of SDEs Through Computer Experiments (2003)
On effects of discretization on estimators of drift parameters for diffusion processes (1996)
The approximation of multiple stochastic integrals (1992)
Construction of stochastic numerical schemes through MAPLE (1993)
Continuous time volatility modelling: COGARCH versus O rnstein- U hlenbeck models (2006)
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High order I to- T aylor approximations to heat kernels (1997)
Weak approximations. A M alliavin calculus approach (2001)
Weak rate of convergence for an E uler scheme of nonlinear SDE s (1997)
Variance reduction methods for simulation of densities on the W iener space (2002)
The E uler scheme for SDE s driven by semimartingales (1994)
A numerical analysis of some first order stochastic initial value problems (1974)
Evaluating and extending the Lee-Carter model for mortality forecasting: B ootstrap confidence interval (2006)
Applied Theory of Fundamental Differential Equations (1992)
Grundbegriffe der Wahrscheinlichkeitsrechnung (1933)
Introductory Real Analysis (1975)
Multi-colored rooted tree analysis of the weak order conditions of a stochastic R unge- K utta family (2007)
Stable ROW -type weak scheme for stochastic differential equations (1995)
Rooted tree analysis of the order conditions of ROW -type scheme for stochastic differential equations (1997)
Some issues in discrete approximate solution for stochastic differential equations (1994)
Edgeworth type expansions for E uler schemes for stochastic differential equations (2002)
Numerical evaluation of path-integrals (1967)
Portfolio optimization with strictly positive transaction costs and impulse control (1994)
Optimal Portfolios (1997)
Value preserving strategies and a general framework for local approaches to optimal portfolios (2001)
On value preserving and growth-optimal portfolios (1999)
The Noether Theorems (2018)
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A jump diffusion model for option pricing (2002)
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An approach to characterizing, modelling and analyzing earthquake excitation records (1977)
Estimation of parameters for systems driven by white noise (1983)
The construction of comparison systems for stochastic differential equations and numerical methods (1986)
The asymptotic elasticity of utility functions and optimal investment in incomplete markets (1999)
Regularization Algorithms for Transistions Matrices (2001)
Arbitrage and equilibrium in economics with infinitely many commodities (1981)
Controlled Diffusion Processes (1980)
Rate of weak convergence of the E uler approximation for diffusion processes with jumps (2002)
Stock returns and hyperbolic distributions (1999)
Langevins stochastic differential equation extended by a time-delayed term (1992)
Strong Discrete Time Approximation of Stochastic Differential Equations with Time Delay (2000)
Weak Discrete Time Approximation of Stochastic Differential Equations with Time Delay (2002)
Time delay and noise explaining cyclical fluctuations in prices of commodities (2007)
Exponential families of stochastic processes: A unifying semimartingale approach (1989)
Exponential Families of Stochastic Processes (1997)
Information Theory and Statistics (1959)
Stochastic differential equations and stochastic flows of diffeomorphisms (1984)
Stochastic flows and stochastic differential equations (1990)
On square-integrable martingales (1967)
Numerische A pproximation von M arkovprozessen (1987)
Weak limit theorems for stochastic integrals and stochastic differential equations (1991)
Wong- Z akai corrections, random evolutions and simulation schemes for SDE s (1991)
Stochastic Stability and Control (1967)
Introduction to Stochastic Control (1971)
On the weak convergence of interpolated M arkov chains to a diffusion (1974)
Probability Methods for Applications in Stochastic Control and for Elliptic Equations (1977)
Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory (1984)
Numerical approximations for nonlinear stochastic systems with delays (2005)
Numerical Methods for Controlled Stochastic Delay Systems (2008)
Approximation for functionals and optimal control on jump diffusion processes (1978)
Numerical Methods for Stochastic Control Problems in Continuous Time (1992)
Approximation of expectation of diffusion process and mathematical finance (2001)
Approximation of expectation of diffusion processes based on L ie algebra and M alliavin calculus (2004)
Parameter Estimation for Stochastic Processes (1984)
Some Questions in the Theory of Numerical Solution of I to Stochastic Differential Equations (1998)
Numerical Modelling of Stochastic Equations and Stochastic Integrals (1999)
Expansion of the S tratonovich multiple stochastic integrals based on the F ourier multiple series (1999)
Stochastic Differential Equations: Theory and Practice of Numerical Solution (2009)
Options on the $M$ best of $N$ risky assets (2000)
Linear and quasilinear equations of parabolic type (1967)
Reconciling differences (1997)
Martingale measure for a class of right-continuous process (1993)
Utility maximization with partial information (1995)
An adaptive timestepping algorithm for stochastic differential equations (2003)
An adaptive Euler-Maruyama scheme for SDEs: C onvergence and stability (2007)
Computational Methods in Ordinary Differential Equations (1973)
Convergence of the critical price in the approximation of A merican options (1993)
Critical price for an A merican option near maturity (1994)
Introduction to Stochastic Calculus Applied to Finance (2007)
Local risk-minimisation under transaction costs (1998)
Bond pricing in a hidden M arkov model of the short rate (2000)
On C ox processes and credit risky bonds (1994)
Pricing risk transfer functions (2000)
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Minimum contrast estimation in diffusion processes (1979)
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Flexible multivariate GARCH modeling with an application to international stock markets (2003)
The Lee-Carter method for forecasting mortality with various extensions and applications (2000)
Modelling and forcasting US mortality (1992)
A G aussian noise generator for hardware-based simulations (2004)
A hardware G aussian noise generator using the B ox- M uller method and its error analysis (2006)
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Adaptive schemes for the numerical solution of SDE s - a comparison (2002)
Binomial models for option valuation - E xamining and improving convergence (1996)
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Stratified sampling and quasi- M onte C arlo simulation of L 'evy processes (2006)
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Approximating systems of differential equations with random inputs or boundary conditions (1998)
A multistep approximation scheme for the L angevin equation (1991)
Approximating the growth optimal portfolio with a diversified world stock index (2006)
On L 'evy processes, M alliavin C alculus and market models with jumps (2006)
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A multistep approximation scheme for the L angevin equation (1939)
Option Valuation Under Stochastic Volatility (2000)
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Effectiveness of implicit methods for stiff stochastic differential equations (2008)
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Approximation of multiple stochastic integrals and its application to stochastic differential equations (1997)
Almost Sure Convergence of the Numerical Discretisation of Stochastic Jump Diffusions (2000)
Lattice models for pricing A merican interest rate claims (1994)
Discretization of jump stochastic differential equations in terms of multiple stochastic integrals (1998)
Convergence and stability of the semi-implicit E uler method for a linear stochastic differential delay equation (2004)
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The variance gamma process and option pricing (1998)
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The multinomial option pricing model and its B rownian and P oisson limits (1989)
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Unifying Black-Scholes type formulae which involve last passage times up to a finite horizon (2008)
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Approximate solution for a class of delay stochastic differential equations (1991)
Exponential Stability of Stochastic Differential Equations (1994)
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Exponential stability of equidistant E uler- M aruyama approximations of stochastic differential delay equations (2007)
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Stabilization and destabilization of hybrid systems of stochastic differential equations (2007)
Stochastic Differential Equations with Markovian Switching (2006)
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Modeling and approximation of stochastic differential equations driven by semimartingales (1981)
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Investment for the long run: N ew evidence for an old rule (1976)
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Valuing guaranteed minimum death benefit options in variable annuities under a benchmark approach (2008)
Expressing a random variable in terms of uniform random variables (1961)
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Families of multivariate distributions (1988)
Stochastic processes for interest rates and equilibrium bond prices (1983)
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Hedging gas bills with weather derivatives (2002)
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Efficient hedging and pricing of equity-linked life insurance contracts on several risky assets (2008)
Margrabe’s formula and quantile hedging of life insurance contracts (2005)
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Option pricing when underlying stock returns are discontinuous (1976)
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Rate of Convergence of the E uler Approximation for Diffusion Processes (1991)
Asset Allocation and annuity-purchase strategies to minimize the probability of financial ruin (2006)
The T itanic Option: V aluation of the Guaranteed Minimum Death Benefit in Variable Annuities and Mutual Funds (2001)
Mortality derivatives and the option to annuities (2001)
The real option to lapse and the valuation of death-protected investments (2001)
Financial valuation of guaranteed minimum withdrawal benefits (2006)
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Analytic pricing of contingent claims under the real world measure (2008)
Real-world pricing for a modified constant elasticity of variance model (2009)
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Weak approximation of solutions of systems of stochastic differential equations (1985)
A theorem on the order of convergence of mean-square approximations of solutions of systems of stochastic differential equations (1987)
Numerical Integration of Stochastic Differential Equations (1988)
A theorem of the order of convergence of mean square approximations of systems of stochastic differential equations (1988)
Numerical Integration of Stochastic Differential Equations (1995)
The solving of boundary value problems by numerical integration of stochastic equations (1995)
Solving the first boundary value problem of parabolic type by numerical integration of stochastic differential equations (1995)
Application of numerical integration of stochastic equations for solving boundary value problems with N eumann boundary conditions (1996)
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The integration of stiff stochastic differential equations with stable second moments (1994)
Balanced implicit methods for stiff stochastic systems (1998)
Numerical methods for stochastic systems preserving symplectic structure (2002)
Monte- C arlo construction of hedging strategies against multi-asset E uropean claims (2002)
Mean-square numerical methods for \sdes with small noises (1994)
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Numerical methods in the weak sense for stochastic differential equations with small noise (1997)
Numerical algorithms for semilinear parabolic equations with small parameter based on approximation of stochastic equations (2000)
Evaluation of conditional W iener integrals by numerical integration of stochastic differential equations (2004)
Stochastic Numerics for Mathematical Physics (2004)
An arbitrage theory of the term structure of interest rates (1994)
Commodity price modelling that matches current observables: A new approach (2002)
Pricing rate of return guarantees in a HJM framework (1999)
Closed form solutions for term structure derivatives with log-normal interest rates (1997)
Pricing of Options on Commodity Futures with Stochastic Term Structure of Convenience Yields and Interest Rates (1998)
A L ie algebraic approach to numerical integration of stochastic differential equations (2001)
Stochastic Calculus for Fractional Brownian Motion and Related Processes (2008)
An Extension of the L' e vy Characterization to Fractional Brownian Motion (2011)
Variable annuity minimum death benefits: A Monte Carlo pricing approach (1994)
Stability analysis of numerical solution of stochastic differential equations (1995)
Financial market meltdown and a need for new financial regulations (2009)
Stochastic modelling of a biochemical reactor (1987)
Geometric L 'evy process pricing model (2002)
Risk-minimizing hedging strategies for unit-linked life insurance contracts (1998)
Risk-minimizing hedging strategies for insurance payment processes (2001)
Hedging equity-linked life insurance contracts (2002)
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Simulations of transaction costs and optimal rehedging (1994)
Stochastic functional differential equations (1984)
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Lyapunov exponents and stochastic flows of linear and affine hereditary systems (1990)
Lyapunov exponents and stationary solutions for affine stochastic delay equations (1990)
Pricing equity-linked pure endowments via the principle of equivalent utility (2003)
Weak exponential schemes for stochastic differential equations with additive noise (2005)
Adaptive weak approximation of diffusions with jumps (2008)
Elements of Simulation (1984)
Low discrepancy sequences generated by piecewise linear maps (1998)
Mathematical problems of modelling stochastic nonlinear dynamical systems (1969)
Optimal portfolio management with fixed transaction costs (1993)
Equilibrium in a capital asset market (1966)
Aspects of Multivariate Statistical Theory (1982)
Optimal design for approximating the path of a stochastic process (1996)
The optimal uniform approximation of systems of stochastic differential equations (2002)
Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis (1990)
Hill, bootstrap and jackknife estimators for heavy tails (1998)
Nominal annual rates and lognormal volatility structure (1994)
General framework for pricing derivative securities (1995)
Martingale Methods in Financial Modelling (2005)
Indifference prices of early exercise claims (2004)
Modelling fluctuations of financial time series: from cascade process to stochastic volatility model (2000)
The pricing of the A merican option (1992)
Linear Differential Equations with Retarded Argument (1972)
Risk-sensitive dynamic portfolio optimization with partial information on infinite time horizon (2002)
Minimization of shortfall risk in a jump-diffusion model (2004)
Approximation of BSDEs by stochastic differential equations (2002)
Numerical procedures for sample structures on stochastic differential equations (1990)
Pricing and Hedging Index Options under Stochastic Volatility: A n Empirical Examination (1996)
2004 Annuity Fact Book (2004)
An Introduction to Copulas (1999)
ARCH models as diffusion approximations (1990)
Conditional Heteroskedasticity in Asset Returns: A New Approach (1991)
The Theory of Games and Economic Behavior (1953)
Discrete Approximations for Markov Chains (1984)
An asymptotic efficient difference formula for solving stochastic differential equations (1986)
Asymptotically optimal discrete approximations for stochastic differential equations (1986)
An efficient approximation for stochastic differential equations on the partition of symmetrical first passage times (1990)
Asymptotically efficient R unge- K utta methods for a class of I to and S tratonovich equations (1991)
Variance reduction for simulated diffusions (1994)
Numerical methods for stochastic differential equations (1996)
Variance reduced M onte C arlo methods for PDEs (1996)
Continuous-time M onte C arlo methods and variance reduction (1997)
On the use and interpolation of certain test criteria for purposes of statistical inference (1928)
Remarks on nonlinear pseudo random numbers (1988)
Low-discrepancy and low-dispersion sequences (1988)
Random Number Generation and Quasi- M onte- C arlo Methods (1992)
M onte C arlo and Quasi-Monte Carlo Methods in Scientific Computing (1995)
Equity-linked life insurance: A model with stochastic interest rates (1995)
Uniqueness of the fair premium of the equity-linked life insurance contracts (1996)
Asian exchange rate options under stochastic interest rates: P ricing as a sum of delayed options (2002)
Pricing bound on A sian options (2003)
The fair premium of an equity-linked life and pension insurance (2008)
Sharpe ratios and alphas in continuous time (2004)
Stochastic trends and jumps in EMS exchange rates (1994)
An essay on the general theory of stochastic processes (2006)
Enlargements of filtrations and path decompositions at non stopping times (2006)
Some random times and martingales associated with BES $_0(\delta)$ processes $(0<\delta<2)$ (2006)
On honest times in financial modeling (2008)
Doob’s maximal identity, multiplicative decompositions and enlargements of filtrations (2006)
Methods of numerical modelling of stochastic differential equations and estimates of their error (1978)
Weak approximation of \sdes and application to derivative pricing (2008)
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Estimation of the parameters of diffusion process (1972)
Sequential estimation of the parameters of diffusion type processes (1972)
On an identity for stochastic integrals (1972)
On estimates and the asymptotic behaviour of nonexit probabilities of a W iener process to a moving boundary (1979)
A first passage problem for autoregression processes and an application to a change-point problem (1990)
Approximations for boundary crossing probabilities (1998)
Chaotic and predictable representations for L 'evy processes (2000)
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Distributional properties of portfolio weights. (2006)
Stochastic portfolio theory optimization and the origin of rule-based investing. (2015)
Malliavin’s calculus and stochastic integral representation of functions of diffusion processes (1984)
A generalized C lark representation formula, with application to optimal portfolios (1991)
Monte C arlo simulation of nonlinear diffusion processes (1992)
Monte C arlo simulation of nonlinear diffusion processes II (1994)
Some problems in the simulation of nonlinear diffusion processes (1995)
Numerical Modelling of Random Processes and Fields: Algorithms and Applications (1996)
Market Microstructure Theory (1995)
Stochastic Differential Equations. An Introduction with Applications (1998)
Applied stochastic control of jump-duffusions (2005)
Applications of Lie Groups to Differential Equations (1993)
The valuation of A merican put options with exponential exercise policies (1987)
Efficient Discrete Time Jump Process models in option pricing (1988)
Brownian Motion in the Stock Market (1959)
Japanese interest rates enter negative territory (1998)
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A bridge between nonlinear time series models and nonlinear stochastic dynamical systems: A local linearization approach (1992)
Utility based optimal hedging in incomplete markets (2001)
The econometrics of financial markets (1995)
Sequences with low discrepancy and pseudo-random numbers: T heoretical remarks and numerical tests (1997)
The jump risk-premia implicit in options: A n integrated time-series study (2002)
Almost sure and moment exponential stability of E uler- M aruyama discretizations for hybrid stochastic differential equations (2008)
Actuaries, accountants and valuations (2000)
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Asymptotic theory of mixing stochastic differential equations (1974)
Probability, Random Variables and Stochastic Processes (1984)
Study of the stability of the solution of a bilinear SDE with periodic coefficients. Application to the motion of helicopter blades (1984)
Discretization and simulation of stochastic differential equations (1985)
Stability of nonlinear differential systems with parametric excitation (1988)
Option pricing: T he A merican put (1977)
Stochastic Processes (1962)
Faster valuation of financial derivatives (1995)
Comparing asset pricing models: A n investment perspective (2000)
A test of the C ox, I ngersoll, R oss model of the term structure of interest rates using the method of moments (1989)
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Efficient Methods for Valuing Interest Rate Derivatives (2000)
Pricing and hedging guaranteed annuity options via static option replication (2003)
The binomial model and the G reeks (1994)
The valuation of guarantees on pension fund returns (1999)
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Some vectorized random number generators for uniform, normal and P oisson distributions for CRAY X-MP (1988)
Stability and accuracy of simulations for stochastic differential equations (1990)
Lagged F ibonacci series random number generators for the NEC SX-3 (1994)
Some experiments on numerical simulations of stochastic differential equations and a new algorithm (1994)
A general implicit splitting for stabilizing numerical simulations of I to stochastic differential equations (1998)
Approximations for stochastic differential equations with reflecting convex boundaries (1995)
Optimal portfolio in partially observed stochastic volatility models (2001)
Energy Risk: Valuing and Managing Energy Derivatives (1998)
Financial pricing of insurance in the multi-line insurance company (1998)
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Filtering of vector diffusions with low noise (1986)
Nonlinear filtering of one-dimensional diffusions in the case of a high signal-to-noise ratio (1986)
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Fast drift approximated pricing in the BGM model (2004)
Bessel processes and infinitely divisible laws (1981)
Laplace transforms related to excursions of a one-dimensional diffusion (1999)
Accessing the Intel� Random Number Generator with CDSA (1999)
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Weak convergence of approximations of I to integral equations (1980)
Equal or value weighting? I mplications for asset pricing tests. (2014)
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Approximation of first exit times of diffusions and approximate solution of parabolic equations (1983)
Beitr"age zur zeitdiskreten A pproximation von I t^oprozessen (1984)
On first exit times of diffusions (1985)
Derivative free numerical methods for stochastic differential equations (1987)
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Higher-order weak approximation of I t^o diffusions by M arkov chains (1992)
On weak implicit and predictor-corrector methods (1995)
A class of truncated interest rate term structure models (1996)
Explaining interest rate dynamics (1996)
Principles for the Construction of Consistent Market Models (1997)
A short term forward rate model (1997)
A non-linear stochastic volatility model (1997)
A Financial Market Model (1998)
An Introduction to Numerical Methods for Stochastic Differential Equations (1999)
A Short Term Interest Rate Model (1999)
Axiomatic principles for a market model (1999)
On the log-return distribution of index benchmarked share prices (1999)
A minimal share market model with stochastic volatility (1999)
A financial market model with trading volume and stochastic volatility (1999)
Financial modelling with benchmark portfolio (2000)
Risk premia and financial modelling without measure transformation (2000)
A forward rate framework (2000)
A Benchmark Model for Financial Markets (2001)
Derivative pricing with benchmark (2001)
Growth optimal portfolio for diffusion processes with jumps (2001)
Benchmark model with intensity based jumps (2002)
A Benchmark Framework for Integrated Risk Management (2002)
A class of term structure benchmark models (2002)
Arbitrage in continuous complete markets (2002)
An alternative currency market model (2003)
A benchmark model for a diversified world index (2003)
A semimartingale benchmark framework for asset pricing (2003)
A two-factor interest rate term structure minimal market model (2003)
A class of complete benchmark models with intensity based jumps (2004)
Simulation methods for stochastic differential equations (2004)
An alternative interest rate term structure model (2005)
On the role of the growth optimal portfolio in finance (2005)
A parsimonious financial market model (2006)
A benchmark approach to portfolio optimization and derivative pricing (2006)
Asset pricing and portfolio optimization in a jump diffusion market (2006)
Capital asset pricing for markets with intensity based jumps (2006)
A Benchmark Approach to Investing and Pricing. In: (2011)
Simulation methods for stochastic differential equations (2008)
Law of the minimal price (2008)
A Benchmark Approach to Pricing (2008)
A benchmark approach beyond semimartingales (2009)
A benchmark approach to investing and pricing (2009)
A benchmark approach to the valuation of variable annuities (2009)
A fractional self-similar market model (2009)
Real world pricing of long term contracts (2009)
Real world pricing of nonhedgable claims (2009)
Real world pricing via utility indifference pricing (2009)
Real-world modeling of insurance liabilities and analysis of hedge effectiveness (2009)
Entropy-maximizing dynamics of continuous markets (2023)
A stock market model under the benchmark approach (2024)
Benchmark-neutral pricing — → 2407.01542
Entropy-maximizing market dynamics and benchmark-neutral pricing (2025)
Numerical Solution of Stochastic Differential Equations with Jumps in Finance (2010)
A Benchmark Approach to Quantitative Finance (2006)
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Weak convergence of semimartingales and discretization methods (1985)
An approach to bond pricing (1993)
On bond price dynamics (1993)
Pricing via anticipative stochastic calculus (1994)
Price dynamics and information (1994)
Fundamental principles for stock market modelling (1994)
Principles for modelling financial markets (1996)
Empirical evidence on S tudent-$t$ log-returns of diversified world stock indices (2008)
Approximating the numeraire portfolio by diversification (2009)
Quasi-exact approximation of hidden M arkov chain filters (2009)
Simulation of diversified portfolios in a continuous financial market (2009)
Modeling Volatility of Diversified Indices (2012)
Market Efficiency and Growth Optimal Portfolio (2017)
Almost exact simulation of multi-dimensional stochastic volatility models (2010)
Approximating the Num' e raire Portfolio by Naive Diversification (2012)
Simulation of diversified portfolios in continuous financial markets (2012)
Dynamics of a well-diversified equity index (2019)
Approximating the growth optimal portfolio and stock price bubbles (2020)
A Benchmark Approach to Filtering in Finance (2005)
Risk minimization under benchmark pricing (2024)
On smile and skewness (1994)
On feedback effects from hedging derivatives (1998)
A dynamic portfolio approach to asset markets and monetary policy (2012)
Asset Markets and Monetary Policy (2009)
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Benchmarked Risk Minimization (2014)
The num' e raire portfolio and arbitrage in semimartingale models of financial markets. (2006)
Balanced M ilstein Methods for Ordinary SDE s (2005)
A structure for general and specific market risk (2003)
On a T aylor formula for a class of I t^o processes (1982)
Intraday empirical analysis of electricity price behaviour (2004)
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Variance reduced M onte C arlo option pricing for jump diffusion models (2004)
Mathematical Models for the Growth of Human Populations (1973)
Bayesian portfolio selection: A n empirical analysis of the S&P 500 index 1970-1996 (2000)
PDF methods in turbulent reactive flows (1985)
The persistence of volatility and stock market fluctuations (1986)
Hedged Monte-Carlo: Low variance derivative pricing with objective probabilities (2001)
Approximate maximum likelihood estimation of discretely observed diffusion processes (1999)
The Logic of Scientific Discovery (2002)
The distribution of share price changes (1972)
Statistical inference from sampled data for stochastic processes (1988)
Statistical Inference for Diffusion Type Processes (1999)
Risk Aversion in the Small and in the Large (1964)
A compound events model for security prices (1967)
Numerical Recipes in C++. The Art of Scientific Computing (2002)
Approximations of solutions of stochastic differential equations driven by semimartingales (1985)
Stochastic Integration and Differential Equations (2005)
The E uler scheme for L 'evy driven stochastic differential equations (1997)
Approximating the Num' e raire Portfolio by Naive Diversification (2012)
A Tractable Model for Indices Approximating the Growth Optimal Portfolio (2012)
Stochastic Differential Systems: Analysis and Filtering (1987)
A million random digits with 100,000 normal deviates (1955)
Quasi- M onte C arlo methods for numerical integration: C omparison of different low discrepancy sequences (1996)
Levy processes in finance: T heory, numerics and empirical facts (2000)
Mean-square stability of semi-implicit E uler method for linear stochastic differential equations with multiple delays and M arkovian switching (2008)
Mean-square stability of M ilstein method for linear hybrid stochastic delay differential equations (2008)
Mean-square stability of second-order R unge- K utta methods for multi-dimensional linear stochastic differential systems (2008)
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Stochastic Processes and Integration (1979)
Numerical solution of I t^o integral equations (1974)
Approximation of stochastic equations by the splitting up method (1995)
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Deriving benefits from death in frontiers (1996)
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