勷勤数学•专家报告

题      目：Exploratory Utility Maximization Problem with Tsallis Entropy

报  告  人：古嘉雯 副教授  (邀请人：杨舟)

                                              南方科技大学

时      间：6月20日  10：30-11：30

地     点：数科院东楼401

报告人简介:

       古嘉雯，南方科技大学副教授、博士生导师。中山大学本科、香港大学博士、哥本哈根大学博士后。主要研究兴趣包括投资组合选择、配对交易等，其研究成果发表在MOR、SICON等国际期刊上。

摘      要：

       We study expected utility maximization problem with constant relative risk aversion utility function in a complete market under the reinforcement learning framework. To induce exploration, we introduce the Tsallis entropy regularizer, which generalizes the commonly used Shannon entropy. Unlike the classical Merton’s problem, which is always well-posed and admits closed-form solutions, we find that the utility maximization exploratory problem is ill-posed in certain cases, due to over-exploration. With a carefully selected primary temperature function, we investigate two specific examples, for which we fully characterize their well-posedness and provide semi-closed-form solutions. It is interesting to find that one example has the well-known Gaussian distribution as the optimal strategy, while the other features the rare Wigner semicircle distribution, which is equivalent to a scaled Beta distribution. The means of the two optimal exploratory policies coincide with that of the classical counterpart. In addition, we examine the convergence of the value function and optimal exploratory strategy as the exploration vanishes. Finally, we design a reinforcement learning algorithm and conduct numerical experiments to demonstrate the advantages of reinforcement learning. 

          欢迎老师、同学们参加、交流！