Stochastic Processes Seminar

Date: March 21, 2024

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Duy Nguyen, Marist College

Title: Continuous-time optimal investment with portfolio constraints: a reinforcement learning approach

Abstract: In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling constraint and borrowing prohibition. The optimal feedback policy of the exploratory unconstrained classical EU problem is shown to be Gaussian. In the case where the portfolio weight is constrained to a given interval, the corresponding constrained optimal exploratory policy follows a truncated Gaussian distribution. We verify that the closed form optimal solution obtained for logarithmic utility \blue{and quadratic utility} for both unconstrained and constrained situations converges to the non-exploratory expected utility counterpart when the exploration weight goes to zero. Finally, we establish a policy improvement theorem and devise an implementable reinforcement learning algorithm by casting the optimal problem in a martingale framework. Our numerical examples confirm the intuitive understanding that a broader domain of investment opportunities necessitates a higher exploration cost. Notably, when subjected to both short-selling and money borrowing constraints, the exploration cost becomes negligible compared to the unconstrained case.