报告时间：2021年6月24日 9:30-10:30

报告地点：点击链接入会，或添加至会议列表：https://meeting.tencent.com/s/AvlXLlgLhn2j

       会议 ID：759 774 574  会议密码：4321

报告人： Jun Cai (Department of Statistics and Actuarial Science,  University of Waterloo)

摘要: 

   Distributionally robust optimization (DRO) has arisen as an important paradigm for addressing the issue of distributional ambiguity in decision optimization. In its standard form, DRO seeks an optimal solution with respect to the worst-case expected value evaluated based on a set of candidate distributions. In the case where a decision maker is not risk neutral, the most common scheme applied in DRO for capturing the risk attitude is to employ an expected utility functional. In this paper, we propose to address a decision maker’s risk attitude in DRO by following an alternative scheme known as “dual expected utility”. In this scheme, a distortion function is applied to convert physical probabilities into subjective probabilities so that the resulting expectation, called a distorted expectation, captures the decision maker’s risk attitude. Unlike an expected utility functional, which is linear in probability, in the dual scheme, the distorted expectation is generally nonlinear in probability. We distinguish DRO based on distorted expectations by coining the term “distributionally robust risk optimization” (DRRO) and show that DRRO problems can be equally, if not more, tractable to solve as DRO problems based on utility functionals. Our tractability results hold for any distortion function, and hence, our scheme provides more flexibility in capturing more realistic forms of risk attitudes. These include, as an important example, the inverse S-shaped distortion functionals that play a prominent role in cumulative prospect theory (CPT) as well as several other nonconvex risk measures developed more recently. Central to our development is the characterization of the worst-case distributions based on the notion of a convex envelope, which enables us to discover “hidden convexity” in DRRO. We demonstrate through a numerical example that a production manager who overly weights “very good” and “very bad” outcomes may act as if (s)he is risk averse when distributional ambiguity is considered. Worst-case distributions are presented that can provide further explanations of such risk-averse behavior. This talk is based on a joint work with Jonathan Yu-Meng Li and Tiantian Mao 

报告人简介: 

   Jun Cai is Professor of Actuarial Science in the Department of Statistics and Actuarial Science at the University of Waterloo. His research interests include dependence modelling, optimization problems in insurance and finance, risk management for insurance and finance, risk management with model uncertainty. His publications appear in different journals including  Mathematical Finance, Finance and Stochastics, Journal of Risk and Insurance,  Advances in Applied Probability, Journal of Multivariate Analysis, Stochastic Processes and their Applications, Insurance: Mathematics and Economics, ASTIN Bulletin, Scandinavian Actuarial Journal. Jun Cai is the winner of the 2020 Bob Alting von Geusau Prize of the International Actuarial Association (IAA).   He is currently serving as an associate editor for Insurance: Mathematics and Economics and an associate editor for Statistical Theory and Related Fields.

邀请人：王过京