IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v68y2022i11p8368-8385.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.2021.4228
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.2021.4228?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    3. 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.
    4. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
    5. 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.
    6. 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..
    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. Xue Dong He & Steven Kou, 2018. "Profit Sharing In Hedge Funds," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 50-81, January.
    9. 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.
    10. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    11. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    12. Suleyman Basak & Anna Pavlova & Alexander Shapiro, 2007. "Optimal Asset Allocation and Risk Shifting in Money Management," The Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1583-1621, 2007 21.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    18. 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.
    19. 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.
    20. Christopher G. Schwarz, 2012. "Mutual Fund Tournaments: The Sorting Bias and New Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 25(3), pages 913-936.
    21. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xinfu Chen & Yuchao Dong & Wenlin Huang & Jin Liang, 2024. "Optimal Carbon Emission Control With Allowances Purchasing," Papers 2407.08477, arXiv.org.
    2. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.
    3. Bi, Xiuchun & Cui, Zhenyu & Fan, Jiacheng & Yuan, Lvning & Zhang, Shuguang, 2023. "Optimal investment problem under behavioral setting: A Lagrange duality perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shuaijie Qian & Chen Yang, 2023. "Non-Concave Utility Maximization with Transaction Costs," Papers 2307.02178, arXiv.org.
    2. Bi, Xiuchun & Cui, Zhenyu & Fan, Jiacheng & Yuan, Lvning & Zhang, Shuguang, 2023. "Optimal investment problem under behavioral setting: A Lagrange duality perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    3. 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.
    4. Sheng, Jiliang & Wang, Jian & Wang, Xiaoting & Yang, Jun, 2014. "Asymmetric contracts, cash flows and risk taking of mutual funds," Economic Modelling, Elsevier, vol. 38(C), pages 435-442.
    5. Zongxia Liang & Yang Liu & Litian Zhang, 2021. "A Framework of State-dependent Utility Optimization with General Benchmarks," Papers 2101.06675, arXiv.org, revised Dec 2023.
    6. Basak, Suleyman & Makarov, Dmitry, 2012. "Difference in interim performance and risk taking with short-sale constraints," Journal of Financial Economics, Elsevier, vol. 103(2), pages 377-392.
    7. Servaes, Henri & Sigurdsson, Kari, 2022. "The Costs and Benefits of Performance Fees in Mutual Funds," Journal of Financial Intermediation, Elsevier, vol. 50(C).
    8. Li, C. Wei & Tiwari, Ashish & Tong, Lin, 2022. "Mutual fund tournaments and fund Active Share," Journal of Financial Stability, Elsevier, vol. 63(C).
    9. Linlin Ma & Yuehua Tang, 2019. "Portfolio Manager Ownership and Mutual Fund Risk Taking," Management Science, INFORMS, vol. 65(12), pages 5518-5534, December.
    10. Sheng, Jiliang & Xu, Si & An, Yunbi & Yang, Jun, 2021. "Dynamic portfolio strategy by loss-averse fund managers facing performance-induced fund flows," International Review of Financial Analysis, Elsevier, vol. 73(C).
    11. Jennifer Huang & Clemens Sialm & Hanjiang Zhang, 2011. "Risk Shifting and Mutual Fund Performance," The Review of Financial Studies, Society for Financial Studies, vol. 24(8), pages 2575-2616.
    12. Marco Nicolosi & Flavio Angelini & Stefano Herzel, 2018. "Portfolio management with benchmark related incentives under mean reverting processes," Annals of Operations Research, Springer, vol. 266(1), pages 373-394, July.
    13. Emilio Barucci & Gaetano Bua & Daniele Marazzina, 2018. "On relative performance, remuneration and risk taking of asset managers," Annals of Finance, Springer, vol. 14(4), pages 517-545, November.
    14. Alain Bensoussan & Abel Cadenillas & Hyeng Keun Koo, 2015. "Entrepreneurial Decisions on Effort and Project with a Nonconcave Objective Function," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 902-914, October.
    15. Cui, Xuegang & Feltovich, Nick & Zhang, Kun, 2022. "Incentive schemes, framing, and market behaviour: Evidence from an asset-market experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 301-324.
    16. Bin Zou, 2017. "Optimal Investment In Hedge Funds Under Loss Aversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-32, May.
    17. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
    18. Eriksen, Kristoffer W. & Kvaløy, Ola, 2014. "Myopic risk-taking in tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 97(C), pages 37-46.
    19. Taylor, Jonathan, 2003. "Risk-taking behavior in mutual fund tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 50(3), pages 373-383, March.
    20. Aymen Karoui & Iwan Meier, 2015. "A note on sorting bias correction in regression-based mutual fund tournament tests," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 29(1), pages 21-29, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:68:y:2022:i:11:p:8368-8385. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.