题　目：Risk-Sensitive Markov Decision Processes with Long-Run CVaR Criterion

嘉　宾：夏俐 教授 中山大学管理学院

主持人：许欢 教授 上海交通大学安泰经济与管理学院

时　间：2025年6月4日（周三）10:00-11:30

地　点：安泰楼A507室

内容简介：

CVaR (Conditional value at risk) is a risk metric widely used in finance. However, dynamically optimizing CVaR is difficult, because it is not a standard Markov decision process (MDP) and the dynamic programming principle fails. In this talk, we study the infinite-horizon discrete-time MDP with a long-run CVaR criterion, from the view of sensitivity-based optimization. By introducing a pseudo-CVaR metric, we reformulate the problem as a bilevel MDP model and derive a CVaR difference formula that quantifies the difference of long-run CVaR under any two policies. The optimality of deterministic policies is derived. We obtain a so-called Bellman local optimality equation for CVaR, which is a necessary and sufficient condition for locally optimal policies and only necessary for globally optimal policies. A CVaR derivative formula is also derived for providing more sensitivity information. Then we develop a policy iteration type algorithm to efficiently optimize CVaR, which is shown to converge to a local optimum in mixed policy space. Furthermore, based on the sensitivity analysis of our bilevel MDP formulation and critical points, we develop a globally optimal algorithm. The piecewise linearity and segment convexity of the optimal pseudo-CVaR function are also established. Our main results and algorithms are further extended to optimize the mean and CVaR simultaneously. Finally, we conduct numerical experiments relating to portfolio management to demonstrate the main results. Our work sheds light on dynamically optimizing CVaR from a sensitivity viewpoint.

演讲人简介：

夏俐，中山大学管理学院教授，长期从事马氏决策过程、强化学习、排队论、随机博弈等理论研究及其在能源、金融等领域的应用研究。在Automatica、IEEE Transactions on Automatic Control、Mathematics of Operations Research、Production and Operations Management等本领域顶级期刊发表论文20余篇，主持5项国家自然科学基金项目、3项国家重点研发计划子课题、多项华为&腾讯等企业研发项目。担任IEEE Transactions on Automation Science and Engineering、Discrete Event Dynamic Systems等国际权威SCI期刊的副主编（AE），曾获2021年和2014年教育部高等学校自然科学二等奖，2024年广东省哲学社会科学优秀成果奖等学术奖励。

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