Nonconcave Utility Maximization with Portfolio Bounds

Min Dai (), Steven Kou (), Shuaijie Qian () and Xiangwei Wan
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Min Dai: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong; Department of Mathematics, Risk Management Institute, and NUS Chongqing and Suzhou Research Institutes, National University of Singapore, Singapore 119076, Singapore
Steven Kou: Questrom School of Business, Boston University, Boston, Massachusetts 02215
Shuaijie Qian: Department of Mathematics, National University of Singapore, Singapore 119076, Singapore

Management Science, 2022, vol. 68, issue 11, 8368-8385

Abstract: The problems of nonconcave utility maximization appear in many areas of finance and economics, such as in behavioral economics, incentive schemes, aspiration utility, and goal-reaching problems. Existing literature solves these problems using the concavification principle. We provide a framework for solving nonconcave utility maximization problems, where the concavification principle may not hold, and the utility functions can be discontinuous. We find that adding portfolio bounds can offer distinct economic insights and implications consistent with existing empirical findings. Theoretically, by introducing a new definition of viscosity solution, we show that a monotone, stable, and consistent finite difference scheme converges to the value functions of the nonconcave utility maximization problems.

Keywords: portfolio constraints; behavioral economics; incentive schemes; concavification principle (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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