Optimization Methods

We study affine stochastic Volterra equations on the cone of symmetric positive semidefinite matrices. For scalar kernels acting entrywise on the matrix dynamics, we establish weak existence by exploiting stochastic invariance results for Volterra equations on convex domains and derive a conditional

Signal correlation and PnL correlation are correlations over different index sets - across assets at each date versus across dates for scalar payoffs - and practitioners often treat the first as a proxy for the second. We give an exact decomposition that shows what that proxy sees and what it discar

This paper is concerned with Merton’s portfolio optimization problem in a Volterra stochastic environment described by a multivariate fake stationary Volterra–Heston model. Due to the non-Markovianity and non-semimartingality of the underlying processes, the classical stochastic control approach ca

The deviation of the efficient market hypothesis (EMH) for the practical economic system allows us gain the arbitrary or risk premium in finance markets. We propose the triplet $(R,H,σ)$ theory to give the local and global optimal portfolio, which eneralize from the $(R,σ)$ model. We present the for

We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional case to the 2-dimensional setting and is applicable for general

We consider the problem of optimal annuitization with labour income, where an agent aims to maximize utility from consumption and labour income under age-dependent force of mortality. Using a dynamic programming approach, we derive closed-form solutions for the value function and the optimal consump

This paper investigates the interactions among consumption/savings, investment, and retirement choices with income disaster. We consider low-income people who are exposed to income disaster so that they retire involuntarily when income disaster occurs. The government provides extra income support to

We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which assume constant volatility. Constructing the optimal portfolio

This paper studies the competition among multiple fund managers with relative performance over the excess logarithmic return. Fund managers compete with each other and have expected utility or mean-variance criteria for excess logarithmic return. Each fund manager possesses a unique risky asset, and

We consider an optimal investment-consumption problem for a utility-maximizing investor who has access to assets with different liquidity and whose consumption rate as well as terminal wealth are subject to lower-bound constraints. Assuming utility functions that satisfy standard conditions, we deve

We investigate exploratory randomization for an extended linear-exponential-quadratic-Gaussian (LEQG) control problem in discrete time. This extended control problem is related to the structure of risk-sensitive investment management applications. We introduce exploration through a randomization of

This paper studies dynamic mean-variance (MV) asset allocation problems in general incomplete markets. Besides of the conventional MV objective on portfolio’s terminal wealth, our framework can accommodate running MV objectives with general (non-exponential) discounting factors while in general, any

Predicting the movement of the stock market and other assets has been valuable over the past few decades. Knowing how the value of a certain sector market may move in the future provides much information for investors, as they use that information to develop strategies to maximize profit or minimize

This note discusses some of the aspects of a model for the covariance of equity returns based on a simple “isotropic” structure in which all pairwise correlations are taken to be the same value. The effect of the structure on feasible values for the common correlation of returns and on the “effectiv

We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to robustness captured by the homothetic multiplier robust speci

In this article, a geometric approach to incorporating investor views in portfolio construction is presented. In particular, the proposed approach utilizes the notion of generalized Wasserstein barycenter (GWB) to combine the statistical information about asset returns with investor views to obtain

This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties a

Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in frac

In an effort to improve the accuracy of credit lending decisions, many financial intuitions are now using predictions from machine learning models. While such predictions enjoy many advantages, recent research has shown that the predictions have the potential to be biased and unfair towards certain

This paper presents a portfolio construction process, including mainly two parts, Factors Selection and Weight Allocations. For the factors selection part, We have chosen 20 factors by considering three aspects, the global market, different assets class, and stock idiosyncratic characteristics. Each

This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals ab

We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston’s stochastic volatility model. We apply the duality methods developed in previous work to obtain a closed-form expression for the optimal portfolio alloca

Market traders often engage in the frequent transaction of volatile assets to optimize their total return. In this study, we introduce a novel investment strategy model, anchored on the ’lazy factor.’ Our approach bifurcates into a Price Portfolio Forecasting Model and a Mean-Variance Model with Tra

This paper presents a comparative analysis of the performances of three portfolio optimization approaches. Three approaches of portfolio optimization that are considered in this work are the mean-variance portfolio (MVP), hierarchical risk parity (HRP) portfolio, and reinforcement learning-based por

When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems involving multiple constraints. To address these challenges,

This paper studies the multi-period mean-variance portfolio allocation problem with transaction costs. Many methods have been proposed these last years to challenge the famous uni-period Markowitz strategy.But these methods cannot integrate transaction costs or become computationally heavy and hardl

The proliferation of diverse, high-leverage trading instruments in modern financial markets presents a complex, “noisy” environment, leading to a critical question: which trading strategies are evolutionarily viable? To investigate this, we construct a large-scale agent-based model, “MAS-Utopia,” co

We investigate the performance of the Kelly rule in a setting in which the dynamics of the return is represented by a time change process. We find that in this general semi-martingale setting the Kelly rule does not maximize the average growth rate, unless the log-return is normally distributed. Nam

For a covariance matrix coming from a factor model of returns, we investigate the relationship between the long-only global minimum variance portfolio and the asset exposures to the factors. In the case of a 1-factor model, we provide a rigorous and explicit description of the long-only solution in

The advancement of large language models (LLMs) has accelerated the development of autonomous financial trading systems. While mainstream approaches deploy multi-agent systems mimicking analyst and manager roles, they often rely on abstract instructions that overlook the intricacies of real-world wo

This paper addresses a key challenge in CDO modeling: achieving a perfect fit to market prices across all tranches using a single, consistent model. The existence of such a perfect-fit model implies the absence of arbitrage among CDO tranches and is thus essential for unified risk management and the

This study develops a strategic procurement framework integrating blockchain-based smart contracts with bounded demand variability modeled through a truncated normal distribution. While existing research emphasizes the technical feasibility of smart contracts, the operational and economic implicatio

We investigate whether large language models can discover and analyze U.S. tax-minimization strategies. This real-world domain challenges even seasoned human experts, and progress can reduce tax revenue lost from well-advised, wealthy taxpayers. We evaluate the most advanced LLMs on their ability to

In this paper, we study an investor’s optimal entry and exit decisions in a liquid staking protocol (LSP) and an automated market maker (AMM), primarily from the standpoint of the investor. Our analysis focuses on two key investor actions: the initial allocation decision at time $t=0$, and the optim

Quantilized mean-field game models involve quantiles of the population’s distribution. We study a class of such games with a capacity for ranking games, where the performance of each agent is evaluated based on its terminal state relative to the population’s $α$-quantile value, $α\in (0,1)$. This ev

Due to the recent increase in interest in Financial Technology (FinTech), applications like credit default prediction (CDP) are gaining significant industrial and academic attention. In this regard, CDP plays a crucial role in assessing the creditworthiness of individuals and businesses, enabling le

A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the p

Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here, we propose a four-step numerical framework for the optimal po

Retail sales and price projections are typically based on time series forecasting. For some product categories, the accuracy of demand forecasts achieved is low, negatively impacting inventory, transport, and replenishment planning. This paper presents our findings based on a proactive pilot exercis

Recently, there are many trials to apply reinforcement learning in asset allocation for earning more stable profits. In this paper, we compare performance between several reinforcement learning algorithms - actor-only, actor-critic and PPO models. Furthermore, we analyze each models’ character and t

In the financial system, bailout strategies play a pivotal role in mitigating substantial losses resulting from systemic risk. However, the lack of a closed-form objective function to the optimal bailout problem poses significant challenges in its resolution. This paper conceptualizes the optimal ba

This paper studies an $α$-robust utility maximization problem where an investor faces an intractable claim – an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market returns. The $α$-robust criterion interpolates between worst-case ($

This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and statistical estimation. The RQ features four stochastics-oriented functionals – risk, deviation, regret, and error, alon

We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the baseline risk measure. We prove continuity in the neighborhood radi

We consider the problem of active portfolio management, where an investor seeks the portfolio with maximal expected utility of the difference between the terminal wealth of their strategy and a proportion of the benchmark’s, subject to a budget and a deviation constraint from the benchmark portfolio

We study continuous-time portfolio choice with nonlinear payoffs under smooth ambiguity and Bayesian learning. We develop a general framework for dynamic, non-concave asset allocation that accommodates nonlinear payoffs, broad utility classes, and flexible ambiguity attitudes. Dynamic consistency is

We develop spectral portfolio theory by establishing a direct identification: neural network weight matrices trained on stochastic processes are portfolio allocation matrices, and their spectral structure encodes factor decompositions and wealth concentration patterns. The three forces governing sto

We study submodularity for law-invariant functionals, with particular attention to convex risk measures. Expected losses are modular, and certainty equivalents are submodular exactly when the loss function is convex. Law-invariant coherent risk measures are submodular exactly when they are coherent

This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the insurance companies under a Bonus-Malus System (BMS) framew

Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event probabilities subject to such distributional model risk. Spec

This paper investigates how Large Language Models (LLMs) from leading providers (OpenAI, Google, Anthropic, DeepSeek, and xAI) can be applied to quantitative sector-based portfolio construction. We use LLMs to identify investable universes of stocks within S&P 500 sector indices and evaluate how the

We consider an agent who has access to a financial market, including derivative contracts, who looks to maximise her utility. Whilst the agent looks to maximise utility over one probability measure, or class of probability measures, she must also ensure that the mark-to-market value of her portfolio

We study a continuous-time portfolio choice problem for an investor whose state-dependent preferences are determined by an exogenous factor that evolves as an Itô diffusion process. Since risk attitudes at the end of the investment horizon are uncertain, terminal wealth is evaluated under a set of u

This paper studies Pareto-optimal reinsurance design in a monopolistic market with multiple primary insurers and a single reinsurer, all with heterogeneous risk preferences. The risk preferences are characterized by a family of risk measures, called Range Value-at-Risk (RVaR), which includes both Va

We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein distance to a reference distribution. We first examine very

We propose and analyze a framework for discrete-time robust mean-field control problems under common noise uncertainty. In this framework, the mean-field interaction describes the collective behavior of infinitely many cooperative agents’ state and action, while the common noise – a random disturba

We apply the theory of McKean-Vlasov-type SDEs to study several problems related to market efficiency in the context of partial information and partially observable financial markets: (i) convergence of reduced-information market price processes to the true price process under an increasing informat

Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable conditional distributions from limited data is notoriously d

In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is characterized solely by a ball determined by general Wasserst

Stablecoins promise par convertibility, yet issuers must balance immediate liquidity against yield on reserves to keep the peg credible. We study this treasury problem as a continuous-time control task with two instruments: reallocating reserves between cash and short-duration government bills, and

Extreme volatility, nonlinear dependencies, and systemic fragility are characteristics of cryptocurrency markets. The assumptions of normality and centralized control in traditional financial risk models frequently cause them to miss these changes. Four components-volatility stress testing, stableco

We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determin

We present a continuous-time portfolio selection framework that reflects goal-based investment principles and mental accounting behavior. In this framework, an investor with multiple investment goals constructs separate portfolios, each corresponding to a specific goal, with penalties imposed on fun

Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality constraint: only $k$ assets from a universe of $p$ may be include

We study the problem of resource provisioning under stringent reliability or service level requirements, which arise in applications such as power distribution, emergency response, cloud server provisioning, and regulatory risk management. With chance-constrained optimization serving as a natural st

We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when the images of these sets under scalar-valued aggregation func

Fundamental and necessary principles for achieving efficient portfolio optimization based on asset and diversification dynamics are presented. The Commonality Principle is a necessary and sufficient condition for identifying optimal drivers of a portfolio in terms of its diversification dynamics. Th

Cross-validation is a statistical tool that can be used to improve large covariance matrix estimation. Although its efficiency is observed in practical applications and a convergence result towards the error of the non linear shrinkage is available in the high-dimensional regime, formal proofs that

Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal dynamic portfolio choice for the MMV utility in asset price

In this paper, we introduce a robust market making framework based on Wasserstein distance, utilizing a stochastic policy approach enhanced by entropy regularization. We demonstrate that, under mild assumptions, the robust market making problem can be reformulated as a convex optimization question.

We propose a constructive framework for the super-hedging problem of a European contingent claim under proportional transaction costs in discrete time. Our main contribution is an explicit recursive scheme that computes both the super-hedging price and the corresponding optimal strategy without rely

Currency arbitrage capitalizes on price discrepancies in currency exchange rates between markets to produce profits with minimal risk. By employing a combinatorial optimization problem, one can ascertain optimal paths within directed graphs, thereby facilitating the efficient identification of profi

Community detection, also known as graph partitioning, is a well-known NP-hard combinatorial optimization problem with applications in diverse fields such as complex network theory, transportation, and smart power grids. The problem’s solution space grows drastically with the number of vertices and

The monotone mean-variance (MMV) preference proposed by Maccheroni, et al. (Math. Finance 19(3): 487-521, 2009) fails to differentiate strictly dominant payoffs, which may cause inconsistency in portfolio decision-making. This paper introduces a broader class of strictly monotone mean-variance (SMMV

As the increasing application of AI in finance, this paper will leverage AI algorithms to examine tail risk and develop a model to alter tail risk to promote the stability of US financial markets, and enhance the resilience of the US economy. Specifically, the paper constructs a multivariate multile

We study the relationship between model complexity and out-of-sample performance in the context of mean-variance portfolio optimization. Representing model complexity by the number of assets, we find that the performance of low-dimensional models initially improves with complexity but then declines

In the data-driven world of actuarial science, machine learning (ML) plays a crucial role in predictive modeling, enhancing risk assessment and pricing strategies. Neural networks, specifically combined actuarial neural networks (CANN), are vital for tasks such as mortality forecasting and pricing.

This paper studies the pricing of contingent claims of American style, using indifference pricing by fully dynamic convex risk measures. We provide a general definition of risk-indifference prices for buyers and sellers in continuous time, in a setting where buyer and seller have potentially differe

This thesis explores the historical progression and theoretical constructs of financial mathematics, with an in-depth exploration of Stochastic Calculus as showcased in the Binomial Asset Pricing Model and the Continuous-Time Models. A comprehensive survey of stochastic calculus principles applied t

The standard approach for constructing a Mean-Variance portfolio involves estimating parameters for the model using collected samples. However, since the distribution of future data may not resemble that of the training set, the out-of-sample performance of the estimated portfolio is worse than one

In this paper, we investigate the robust models for $Λ$-quantiles with partial information regarding the loss distribution, where $Λ$-quantiles extend the classical quantiles by replacing the fixed probability level with a probability/loss function $Λ$. We find that, under some assumptions, the robu

Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, we prove that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, we find sharp bounds in this class for many aggregate risk measures, s

We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a Brownian diffusion with affine drift, and convex volatility. We pro

The $\ell_0$-constrained mean-CVaR model poses a significant challenge due to its NP-hard nature, typically tackled through combinatorial methods characterized by high computational demands. From a markedly different perspective, we propose an innovative autonomous sparse mean-CVaR portfolio model,

This paper establishes that conditioning the probability of execution of new orders on the self-generated historical trading information (HTI) of a trading strategy is a necessary condition for a statistical trading edge. It is shown, in particular, that, given any trading strategy S that does not u

This study addresses limited attention allocation in a stochastic linear quadratic system with multiplicative noise. Our approach enables strategic resource allocation to enhance noise estimation and improve control decisions. We provide analytical optimal control and propose a numerical method for

This paper studies the market structure impact of cheaper and faster chains on the Uniswap v3 Protocol. The Uniswap Protocol is the largest decentralized application on Ethereum by both gas and blockspace used, and user behaviors of the protocol are very sensitive to fluctuations in gas prices and m

This paper comprehensively reviews the application of machine learning (ML) and AI in finance, specifically in the context of asset pricing. It starts by summarizing the traditional asset pricing models and examining their limitations in capturing the complexities of financial markets. It explores h

Convex optimisation has provided a mechanism to determine arbitrage trades on automated market markets (AMMs) since almost their inception. Here we outline generic closed-form solutions for $N$-token geometric mean market maker pool arbitrage, that in simulation (with synthetic and historic data) pr

In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton–Jacobi–Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic control may be undesirable for various business reasons. In this

We develop a efficient, easy-to-implement, and strictly monotone numerical integration method for Mean-Variance (MV) portfolio optimization in realistic contexts, which involve jump-diffusion dynamics of the underlying controlled processes, discrete rebalancing, and the application of investment con

This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member’s aim is to maximize the expected utility

This paper introduces the concept of a global financial market for environmental indices, addressing sustainability concerns and aiming to attract institutional investors. Risk mitigation measures are implemented to manage inherent risks associated with investments in this new financial market. We m

We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a seamless substitution for traditional neural networks. This approa

Linear regression, firstly introduced for the pricing of American-style options, has since been expanded to include swing options pricing. Swing options price may be viewed as the solution to a Backward Dynamic Programming Principle, which involves a conditional expectation known as the continuation

This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We establish a proper theoretical characterization of this problem vi

Market making of options with different maturities and strikes is a challenging problem due to its highly dimensional nature. In this paper, we propose a novel approach that combines a stochastic policy and reinforcement learning-inspired techniques to determine the optimal policy for posting bid-as

The over-the-counter (OTC) market is characterized by a unique feature that allows market makers to adjust bid-ask spreads based on order size. However, this flexibility introduces complexity, transforming the market-making problem into a high-dimensional stochastic control problem that presents sig

In this paper, we provide an overview of the recent work in the quantum finance realm from various perspectives. The applications in consideration are Portfolio Optimization, Fraud Detection, and Monte Carlo methods for derivative pricing and risk calculation. Furthermore, we give a comprehensive ov

The US stock market experienced instability following the recession (2007-2009). COVID-19 poses a significant challenge to US stock traders and investors. Traders and investors should keep up with the stock market. This is to mitigate risks and improve profits by using forecasting models that accoun