IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.19259.html
   My bibliography  Save this paper

Time-Consistent Portfolio Selection for Rank-Dependent Utilities in an Incomplete Market

Author

Listed:
  • Jiaqin Wei
  • Jianming Xia
  • Qian Zhao

Abstract

We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium strategies. In the case of time-invariant probability weighting function, we provide a comprehensive characterization of the deterministic strict equilibrium strategy. The unique non-zero equilibrium, if exists, can be determined by solving an autonomous ODE. In the case of time-variant probability weighting functions, we observe that there may be infinitely many non-zero deterministic strict equilibrium strategies, which are derived from the positive solutions to a nonlinear singular ODE. By specifying the maximal solution to the singular ODE, we are able to identify all the positive solutions. In addition, we address the issue of selecting an optimal strategy from the numerous equilibrium strategies available.

Suggested Citation

  • Jiaqin Wei & Jianming Xia & Qian Zhao, 2024. "Time-Consistent Portfolio Selection for Rank-Dependent Utilities in an Incomplete Market," Papers 2409.19259, arXiv.org.
    • Handle: RePEc:arx:papers:2409.19259
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.19259
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
    2. Wei, Jiaqin & Wang, Tianxiao, 2017. "Time-consistent mean–variance asset–liability management with random coefficients," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 84-96.
    3. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    4. Jianming Xia & Xun Yu Zhou, 2016. "Arrow–Debreu Equilibria For Rank-Dependent Utilities," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 558-588, July.
    5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    6. repec:dau:papers:123456789/5392 is not listed on IDEAS
    7. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    8. repec:dau:papers:123456789/2317 is not listed on IDEAS
    9. Yu-Jui Huang & Zhenhua Wang, 2020. "Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems," Papers 2006.00754, arXiv.org, revised Jan 2021.
    10. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2017. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Post-Print hal-01139343, HAL.
    11. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    12. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    13. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    14. Zongxia Liang & Sheng Wang & Jianming Xia & Fengyi Yuan, 2024. "Dynamic portfolio selection under generalized disappointment aversion," Papers 2401.08323, arXiv.org, revised Mar 2024.
    Full references (including those not matched with items on IDEAS)

    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. Marcel Nutz & Yuchong Zhang, 2019. "Conditional Optimal Stopping: A Time-Inconsistent Optimization," Papers 1901.05802, arXiv.org, revised Oct 2019.
    2. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2021. "Consistent investment of sophisticated rank‐dependent utility agents in continuous time," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1056-1095, July.
    3. Yan, Tingjin & Wong, Hoi Ying, 2020. "Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 105-119.
    4. Zhiping Chen & Liyuan Wang & Ping Chen & Haixiang Yao, 2019. "Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-33, September.
    5. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2020. "Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time," Working Papers hal-02624308, HAL.
    6. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    7. Xue Dong He & Zhaoli Jiang & Steven Kou, 2020. "Portfolio Selection under Median and Quantile Maximization," Papers 2008.10257, arXiv.org, revised Mar 2021.
    8. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    9. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2020. "Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time," Papers 2006.01979, arXiv.org.
    10. Zongxia Liang & Sheng Wang & Jianming Xia & Fengyi Yuan, 2024. "Dynamic portfolio selection under generalized disappointment aversion," Papers 2401.08323, arXiv.org, revised Mar 2024.
    11. Mi, Hui & Xu, Zuo Quan, 2023. "Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 82-105.
    12. Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximization with intractable claims," Papers 2304.06938, arXiv.org, revised Jul 2023.
    13. Zongxia Liang & Fengyi Yuan, 2021. "Equilibrium master equations for time-inconsistent problems with distribution dependent rewards," Papers 2112.14462, arXiv.org, revised Apr 2022.
    14. Bingyan Han & Chi Seng Pun & Hoi Ying Wong, 2023. "Robust Time-inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach," Papers 2306.16982, arXiv.org, revised Sep 2024.
    15. Yushi Hamaguchi & Alex S. L. Tse, 2024. "Periodic portfolio selection with quasi-hyperbolic discounting," Papers 2410.18240, arXiv.org.
    16. Bingyan Han & Hoi Ying Wong, 2019. "Time-inconsistency with rough volatility," Papers 1907.11378, arXiv.org, revised Dec 2021.
    17. Zuo Quan Xu, 2018. "Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework," Papers 1803.02546, arXiv.org, revised Aug 2021.
    18. Xue Dong He & Zhaoli Jiang, 2020. "Optimal Payoff under the Generalized Dual Theory of Choice," Papers 2012.00345, arXiv.org.
    19. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2021. "Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time," Post-Print hal-02624308, HAL.
    20. Wang, Hao & Wang, Rongming & Wei, Jiaqin, 2019. "Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 104-114.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2409.19259. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.