报告题目：Multistage Utility Preference Robust Optimization

主讲嘉宾：西安交通大学刘嘉副教授

讲座时间：2022年12月31日9:00-10:30

讲座方式：腾讯会议（会议号：619-997-737）

邀请人：童小娇

报告摘要：In this talk, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical data and the information on the true utility function is incomplete. To mitigate the risk arising from ambiguity of the true utility, we propose a maximin robust model where the optimal policy is based on the worst sequence of utility functions from an ambiguity set constructed with partially available information about the decision maker's preferences. We then show that the multistage maximin problem is time consistent when the utility functions are state-dependent. With the time consistency, we show the maximin problem can be solved by a recursive formula whereby a one-stage maximin problem is solved at each stage beginning from the last stage. Moreover, we propose two approaches to construct the ambiguity set: a pairwise comparison approach and a $\zeta$-ball approach where a ball of utility functions centered at a nomina utility function under $\zeta$-metric is considered. To overcome the difficulty arising from solving the infinite dimensional optimization problem in computation of the worst-case expected utility value, we propose piecewise linear approximation of the utility functions and derive error bound for the approximation under moderate conditions. Finally, we develop scenario tree-based and dynamic programming based computational scheme for solving the multistage preference robust optimization model and report some preliminary numerical results. This is a joint work with Zhiping Chen and Huifu Xu.

专家简介：刘嘉，西安交通大学数学与统计学院科学计算系副教授。本科、硕士、博士均毕业于西安交通大学，期间赴法国巴黎第11大学联合培养。研究兴趣包括随机优化、鲁棒优化等近现代优化方法，强化学习等人工智能方法，及其在金融工程中的应用。他在这些方向取得了一些研究结果，在Mathematics of Operations Research 、SIAM Journal on Optimization 、European Journal of Operational Research、Quantitative Finance 等运筹学、金融学期刊上发表学术论文30余篇，主持国家自然科学基金青年项目一项，参与国家重点研发计划、国家自然科学基金重大、重点、面上项目及横向课题十余项。