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Nonconcave Utility Maximization with Portfolio Bounds

Author

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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)

  • Xiangwei Wan

    (Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China)

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.

Suggested Citation

  • Min Dai & Steven Kou & Shuaijie Qian & Xiangwei Wan, 2022. "Nonconcave Utility Maximization with Portfolio Bounds," Management Science, INFORMS, vol. 68(11), pages 8368-8385, November.
    • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:11:p:8368-8385
    DOI: 10.1287/mnsc.2021.4228
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    References listed on IDEAS

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    Cited by:

    1. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.

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