This hub holds the mathematical engine room of quantitative finance: stochastic control (choose a policy that steers a diffusion), optimal stopping (choose a time to act), and the machinery that solves them — Hamilton–Jacobi–Bellman equations, viscosity solutions, backward stochastic differential equations, and mean-field games for the many-player limit. The classic applications are Merton-style consumption and investment, optimal liquidation, dividend and reinsurance control, and American-option exercise.
Most papers here are Lab Rats by our scoring: deep theory, little or no data. That is not a criticism of the work, but it changes how you read it. The questions that matter are whether the model’s state variables are observable in practice, whether the closed-form or numerical solution degrades gracefully when parameters are estimated rather than known, and whether a paper that claims a strategy ever confronts it with transaction costs or discrete rebalancing. The handful of papers that pair a control result with a calibrated numerical study rank highest below.
Related hubs: Options & Derivatives, Portfolio Optimization, HFT & Optimal Execution, Insurance & Actuarial Risk.
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
This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients’ investment preferences from past activities. Our approach leverages a continuous-time model that incorporates utility functions
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
In this paper, we explore the use of a deep residual U-net with self-attention to solve the the continuous time time-consistent mean variance optimal trade execution problem for multiple agents and assets. Given a finite horizon we formulate the time-consistent mean-variance optimal trade execution
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic control problem, as the admissible control depends on its o
The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent’s goal is to maximize an objective functional associated with his profit-and-loss of trading and simultaneously minimize the execution risk and the marke
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
We study an implementation of the theoretical splitting scheme introduced in [Chassagneux and Yang, 2022] for singular FBSDEs [Carmona and Delarue 2013] and their associated quasi-linear degenerate PDEs. The fully implementable algorithm is based on particles approximation of the transport operator
Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style derivatives and the associated optimal stopping problems. This paper
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
We study the optimal investment problem for a homogeneous collective of $n$ individuals investing in a Black-Scholes model subject to longevity risk with Epstein–Zin preferences. %and with preferences given by power utility. We compute analytic formulae for the optimal investment strategy, consumpt
In this paper, we present Deep-MacroFin, a comprehensive framework designed to solve partial differential equations, with a particular focus on models in continuous time economics. This framework leverages deep learning methodologies, including Multi-Layer Perceptrons and the newly developed Kolmogo
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
We develop a stochastic game-theoretic model for intraday dispatch of grid-scale battery energy storage systems (BESSs). We assume that each BESS operator competitively manages her state-of-charge to maximize energy arbitrage revenues, driven by the endogenized electricity price that depends on the
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 ($
We study a benchmarked risk-sensitive portfolio problem in a factor-based setting to bring together three strands of the literature: benchmarked risk-sensitive investment management, the Kuroda-Nagai change-of-measure method, and the free energy-entropy duality of Dai Pra et al. (1996). We show that
G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation approach within the G-expectation environment, yielding a no
We study market making in aggregator-routed RFQ markets where platform routing depends on slowly varying dealer performance scores. We propose a two-tier stochastic control model that separates RFQ-level price competition from a macro routing layer: tier A represents aggregator flow whose opportunit
We study an OTC FX market-making problem, built on the Avellaneda-Stoikov tradition, in which a dealer streams size-dependent quotes on a discrete ladder and manages inventory risk over a finite horizon under Poisson arrivals of trade requests. Adverse selection is modelled through latency-driven pr