Decision Making Under Cumulative Prospect Theory: An Alternating Direction Method of Multipliers

Xiangyu Cui (), Rujun Jiang (), Yun Shi (), Rufeng Xiao () and Yifan Yan ()
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Xiangyu Cui: School of Statistics and Management, Dishui Lake Advanced Finance Institute, Shanghai University of Finance and Economics, Shanghai 200437, China
Rujun Jiang: School of Data Science, Fudan University, Shanghai 200433, China
Yun Shi: School of Statistics, East China Normal University, Shanghai 200050, China
Rufeng Xiao: School of Data Science, Fudan University, Shanghai 200433, China
Yifan Yan: School of Data Science, Fudan University, Shanghai 200433, China

INFORMS Journal on Computing, 2025, vol. 37, issue 4, 856-873

Abstract: This paper proposes 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, whereas 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.

Keywords: utility optimization; cumulative prospect theory; alternating direction method of multipliers; dynamic programming (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:37:y:2025:i:4:p:856-873

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