IDEAS home Printed from https://ideas.repec.org/a/cuf/journl/y2025v26i1zhuhuangbin.html
   My bibliography  Save this article

Robust Non-zero-sum Asset Allocation Games Under Relative Wealth Concerns

Author

Listed:
  • Huainian Zhu

    (School of Economics, Guangdong University of Technology)

  • Sihan Huang

    (School of Economics, Guangdong University of Technology)

  • Ning Bin

    (School of Management, Guangdong University of Technology)

Abstract

This paper considers the non-zero sum stochastic differential asset allocation game problem between two competitive institutional investors, who are concerned with the potential model ambiguity and aim to seek the robust optimal asset allocation strategy. The two investors' decisions influence each other through the investors' relative wealth concerns. By applying the dynamic programming principle, explicit solutions for the robust equilibrium asset allocation strategies are obtained under the representative case of constant relative risk aversion (CRRA) utility. Finally, we provide some numerical studies and draw some economic interpretations.

Suggested Citation

  • Huainian Zhu & Sihan Huang & Ning Bin, 2025. "Robust Non-zero-sum Asset Allocation Games Under Relative Wealth Concerns," Annals of Economics and Finance, Society for AEF, vol. 26(1), pages 415-441, May.
    • Handle: RePEc:cuf:journl:y:2025:v:26:i:1:zhuhuangbin
    as

    Download full text from publisher

    File URL: http://down.aefweb.net/AefArticles/aef260111ZhuHuangBin.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    2. Man Li & Ying Huang & Ya Huang & Jieming Zhou, 2024. "Robust non-zero-sum stochastic differential game of two insurers with common shock and CDS transaction," Mathematics and Financial Economics, Springer, volume 18, number 3, October.
    3. John H. Cochrane, 1997. "Where is the market going? Uncertain facts and novel theories," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 21(Nov), pages 3-37.
    4. Yulei Luo & Jun Nie & Haijun Wang, 2023. "Ambiguous Consumption and Asset Allocation with Unknown Markovian Income Growth," Annals of Economics and Finance, Society for AEF, vol. 24(2), pages 237-275, November.
    5. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    6. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2020. "Robust Portfolio Optimization with Multi-Factor Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 264-298, July.
    7. Shen, Yang & Zeng, Yan, 2015. "Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 118-137.
    8. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    9. 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.
    10. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    11. Kraft, Holger & Meyer-Wehmann, André & Seifried, Frank Thomas, 2020. "Dynamic asset allocation with relative wealth concerns in incomplete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    12. Suleyman Basak & Dmitry Makarov, 2014. "Strategic Asset Allocation in Money Management," Journal of Finance, American Finance Association, vol. 69(1), pages 179-217, February.
    13. Daniel Lacker & Thaleia Zariphopoulou, 2019. "Mean field and n‐agent games for optimal investment under relative performance criteria," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1003-1038, October.
    14. Sun, Jingyun & Yao, Haixiang & Kang, Zhilin, 2019. "Robust optimal investment–reinsurance strategies for an insurer with multiple dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 157-170.
    15. Weidong Xu & Hongyi Li & Chongfeng Wu, 2011. "A Robust General Equilibrium Stochastic Volatility Model with Recursive Preference Investors," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 217-231, November.
    16. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2019. "Robust non-zero-sum investment and reinsurance game with default risk," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 115-132.
    17. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2019. "Robust portfolio optimization with multi-factor stochastic volatility," Papers 1910.06872, arXiv.org, revised Jun 2020.
    18. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    19. Yulei Luo, 2017. "Robustly Strategic Consumption–Portfolio Rules with Informational Frictions," Management Science, INFORMS, vol. 63(12), pages 4158-4174, December.
    20. Xudong Zeng & Michael Taksar, 2013. "A stochastic volatility model and optimal portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 13(10), pages 1547-1558, October.
    21. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    22. Zeng, Yan & Li, Danping & Chen, Zheng & Yang, Zhou, 2018. "Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 70-103.
    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. Zhu, Huainian & Zhang, Yumo, 2025. "Robust Nash equilibrium for defined contribution pension games with delay under multivariate stochastic covariance models," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 236-268.
    2. Wang, Ning & Zhang, Yumo, 2024. "Robust asset-liability management games for n players under multivariate stochastic covariance models," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 67-98.
    3. Yumo Zhang, 2023. "Robust Optimal Investment Strategies for Mean-Variance Asset-Liability Management Under 4/2 Stochastic Volatility Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-32, March.
    4. Wang, Ning & Zhang, Yumo, 2023. "Robust optimal asset-liability management with mispricing and stochastic factor market dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 251-273.
    5. Wang, Pei & Li, Zhongfei, 2018. "Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 67-83.
    6. Guan, Guohui & Hu, Jiaqi & Liang, Zongxia, 2022. "Robust equilibrium strategies in a defined benefit pension plan game," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 193-217.
    7. Wei, Pengyu & Yang, Charles & Zhuang, Yi, 2023. "Robust consumption and portfolio choice with derivatives trading," European Journal of Operational Research, Elsevier, vol. 304(2), pages 832-850.
    8. Sujoy Mukerji & Han N. Ozsoylev & Jean‐Marc Tallon, 2023. "Trading Ambiguity: A Tale Of Two Heterogeneities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1127-1164, August.
    9. Garces, Len Patrick Dominic M. & Shen, Yang, 2025. "Robust optimal investment and consumption strategies with portfolio constraints and stochastic environment," European Journal of Operational Research, Elsevier, vol. 322(2), pages 693-712.
    10. Han, Jinhui & Ma, Guiyuan & Yam, Sheung Chi Phillip, 2022. "Relative performance evaluation for dynamic contracts in a large competitive market," European Journal of Operational Research, Elsevier, vol. 302(2), pages 768-780.
    11. Horváth, Ferenc, 2017. "Essays on robust asset pricing," Other publications TiSEM e54d7b33-1f27-4b0e-9f84-f, Tilburg University, School of Economics and Management.
    12. Man Li & Ying Huang & Ya Huang & Jieming Zhou, 2024. "Robust non-zero-sum stochastic differential game of two insurers with common shock and CDS transaction," Mathematics and Financial Economics, Springer, volume 18, number 3, October.
    13. Len Patrick Dominic M. Garces & Yang Shen, 2024. "Robust optimal investment and consumption strategies with portfolio constraints and stochastic environment," Papers 2407.02831, arXiv.org.
    14. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2015. "Robust portfolio choice with derivative trading under stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 142-157.
    15. Curatola, Giuliano, 2022. "Price impact, strategic interaction and portfolio choice," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    16. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    17. Luo, Yulei & Nie, Jun & Wang, Haijun, 2022. "Ignorance, pervasive uncertainty, and household finance," Journal of Economic Theory, Elsevier, vol. 199(C).
    18. Zhang, Jinping & Zhou, Lei & Zou, Zhentao, 2024. "Robust dynamic trading with realization utility," Economics Letters, Elsevier, vol. 244(C).
    19. Wujun Lv & Tao Pang & Xiaobao Xia & Jingzhou Yan, 2023. "Dynamic portfolio choice with uncertain rare-events risk in stock and cryptocurrency markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-28, December.
    20. Yan Zhang & Peibiao Zhao & Rufei Ma, 2022. "Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with more General Dependent Claim Risks and Defaultable Risk," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2743-2777, December.

    More about this item

    Keywords

    Robust non-zero-sum game; Asset allocation; Ambiguity; Nash equilibrium; Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G41 - Financial Economics - - Behavioral Finance - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making in Financial Markets

    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:cuf:journl:y:2025:v:26:i:1:zhuhuangbin. 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: Qiang Gao (email available below). General contact details of provider: https://edirc.repec.org/data/emcufcn.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.