报告题目 (Title)：Decision Making under Cumulative Prospect Theory: An Alternating Direction Method of Multipliers （累积前景理论下的决策：一种ADMM方法）

报告人 (Speaker)：江如俊 副教授（复旦大学大数据学院）

报告时间 (Time)：2023年11月7日 (周二) 15:40

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：徐姿 教授

主办部门：理学院数学系

报告摘要：In this talk, I will present a novel numerical method for solving the problem of decision making under cumulative prospect theory (CPT), where the goal is to maximize utility subject to practical constraints, assuming only finite realizations of the associated distribution are available. Existing methods for CPT optimization rely on particular assumptions that may not hold in practice. To overcome this limitation, we present the first numerical method with a theoretical guarantee for solving CPT optimization using an alternating direction method of multipliers (ADMM). One of its subproblems involves optimization with the CPT utility subject to a chain constraint, which presents a significant challenge. To address this, we develop two methods for solving this subproblem. The first method uses dynamic programming, while the second method is a modified version of the pooling-adjacent-violators algorithm that incorporates the CPT utility function. Moreover, we prove the theoretical convergence of our proposed ADMM method and the two subproblem-solving methods. Finally, we conduct numerical experiments to validate our proposed approach and demonstrate how CPT's parameters influence investor behavior using real-world data. I will also talk about an application of the algorithm to rank-based loss minimization in machine learning.