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Nonconcave Utility Maximization with Portfolio Bounds

Author

Listed:
  • 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

    as
    1. Martin B. Haugh & Leonid Kogan & Jiang Wang, 2006. "Evaluating Portfolio Policies: A Duality Approach," Operations Research, INFORMS, vol. 54(3), pages 405-418, June.
    2. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
    3. Vila, Jean-Luc & Zariphopoulou, Thaleia, 1997. "Optimal Consumption and Portfolio Choice with Borrowing Constraints," Journal of Economic Theory, Elsevier, vol. 77(2), pages 402-431, December.
    4. Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
    5. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    6. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    7. Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
    8. Suleyman Basak & Anna Pavlova & Alexander Shapiro, 2007. "Optimal Asset Allocation and Risk Shifting in Money Management," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1583-1621, 2007 21.
    9. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    10. Chen, Honghui & Desai, Hemang & Krishnamurthy, Srinivasan, 2013. "A First Look at Mutual Funds That Use Short Sales," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(3), pages 761-787, June.
    11. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    12. Dai, Min & Jin, Hanqing & Liu, Hong, 2011. "Illiquidity, position limits, and optimal investment for mutual funds," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1598-1630, July.
    13. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    14. Enrico Diecidue & Jeroen van de Ven, 2008. "Aspiration Level, Probability Of Success And Failure, And Expected Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 683-700, May.
    15. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    16. Xue Dong He & Steven Kou, 2018. "Profit Sharing In Hedge Funds," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 50-81, January.
    17. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    18. Busse, Jeffrey A., 2001. "Another Look at Mutual Fund Tournaments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 36(1), pages 53-73, March.
    19. Brown, Keith C & Harlow, W V & Starks, Laura T, 1996. "Of Tournaments and Temptations: An Analysis of Managerial Incentives in the Mutual Fund Industry," Journal of Finance, American Finance Association, vol. 51(1), pages 85-110, March.
    20. Enrico Diecidue & Jeroen Van De Ven, 2008. "Aspiration Level, Probability Of Success And Failure, And Expected Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 683-700, May.
    21. Christopher G. Schwarz, 2012. "Mutual Fund Tournaments: The Sorting Bias and New Evidence," Review of Financial Studies, Society for Financial Studies, vol. 25(3), pages 913-936.
    22. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    23. Agarwal, Vikas & Boyson, Nicole M. & Naik, Narayan Y., 2009. "Hedge Funds for Retail Investors? An Examination of Hedged Mutual Funds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(2), pages 273-305, April.
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