Actuarial Science Seminar: Professor Xunyu Zhou

Zeit : Dienstag , 2:00 pm
Veranstalter : Veranstalter: Universität Ulm, Fachgebiet Wirtschafts- und Steuerrecht und Ulmer Forum für Wirtschaftswissenschaften
Ort : Universität Ulm, Helmholtzstraße 22, 1.42

Professor Xunyu Zhou (, IEOR, Columbia University, will give a talk in our actuarial science seminar. 

Time and Location: July 16, 2024 (Tuesday), 2:00 p.m., Heho 22, Room 1.42

Titel:  Learning Merton’s Strategies in an Incomplete Market: Recursive Entropy Regularization and Biased Gaussian Exploration

Abstract: We study Merton’s expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters. Based on the entropy-regularization framework for general continuous-time RL formulated in Wang et al. (2020), we propose a recursive weighting scheme on exploration that endogenously discounts the current exploration reward by past accumulative amount of exploration. Such a recursive regularization restores the optimality of Gaussian exploration. However, contrary to the existing results, the optimal Gaussian policy turns out to be biased in general, due to the interwinding needs for hedging and for exploration. We present an asymptotic analysis of the resulting errors to show how the level of exploration affects the learned policies. Furthermore, we establish a policy improvement theorem and design several RL algorithms to learn Merton’s optimal strategies. At last, we carry out both simulation and empirical studies with a stochastic volatility environment to demonstrate the efficiency and robustness of the RL algorithms in comparison to the conventional plug-in method.