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This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…
We study the problem of dynamically trading multiple futures whose underlying asset price follows a multiscale central tendency Ornstein-Uhlenbeck (MCTOU) model. Under this model, we derive the closed-form no-arbitrage prices for the…
This paper addresses the model-free nonlinear optimal problem with generalized cost functional, and a data-based reinforcement learning technique is developed. It is known that the nonlinear optimal control problem relies on the solution of…
This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing…
Physics-informed neural solvers offer a promising route to model-based reinforcement learning in continuous time, where optimal feedback synthesis is governed by Hamilton--Jacobi--Bellman (HJB) equations. Practical implementations often…
In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a…
Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…
In this paper we study the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is…
For an infinite-horizon control problem, the optimal control can be represented by the stable manifold of the characteristic Hamiltonian system of Hamilton-Jacobi-Bellman (HJB) equation in a semiglobal domain. In this paper, we first…
With the recent advancements in machine learning (ML), artificial neural networks (ANN) are starting to play an increasingly important role in quantitative finance. Dynamic portfolio optimization is among many problems that have…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…
In this paper, we study optimal liquidation problems in a randomly-terminated horizon. We consider the liquidation of a large single-asset portfolio with the aim of minimizing a combination of volatility risk and transaction costs arising…
This paper extends the classical consumption and portfolio rules model in continuous time (Merton 1969, 1971) to the framework of decision-makers with time-inconsistent preferences. The model is solved for different utility functions for…
This paper, which is the natural continuation of a previous paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes…
We prove the existence of a continuous-time Radner equilibrium with multiple agents and transaction costs. The agents are incentivized to trade towards a targeted number of shares throughout the trading period and seek to maximize their…
We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity…
In this paper, we investigate a constrained optimal coordination problem for a class of heterogeneous nonlinear multi-agent systems described by high-order dynamics subject to both unknown nonlinearities and external disturbances. Each…
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…
This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive…