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Behavioral robust mean-variance portfolio selection with an intractable claim

Author

Listed:
  • Arindam Maity

    (Indian Institute of Technology Guwahati)

  • Koushik Bera

    (Indian Institute of Technology Guwahati)

  • N. Selvaraju

    (Indian Institute of Technology Guwahati)

Abstract

In this article, we study a behavioral robust mean-variance portfolio selection model involving an intractable claim, which may not be directly associated with the underlying financial market but can significantly impact the terminal payoff. Also, an investor often overestimates small probabilities and underestimates large ones due to different attitudes toward gains and losses. This behavioral phenomenon of the investor is captured through a probability distortion function. We simultaneously consider a random variable representing the payoff of the behavioral investor and an intractable claim together in the terminal payoff. The distribution function of the behavioral payoff is a distorted distribution of investment payoff based on the financial market, accounting for the impact of probability distortion. We formulate a robust optimization problem by considering the worst-case scenario among all possible identically distributed random variables representing the intractable claim. By integrating the martingale method and quantile function, we analytically obtain a closed-form optimal solution of the behavioral robust mean-variance model with an intractable claim. Furthermore, we develop a numerical algorithm to compute the efficient frontiers of our models and compare their performances with an existing model that does not incorporate probability distortion.

Suggested Citation

  • Arindam Maity & Koushik Bera & N. Selvaraju, 2025. "Behavioral robust mean-variance portfolio selection with an intractable claim," Mathematics and Financial Economics, Springer, volume 19, number 5, December.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:2:d:10.1007_s11579-025-00386-2
    DOI: 10.1007/s11579-025-00386-2
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    References listed on IDEAS

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    1. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Huang, Xiaoxia & Yang, Tingting, 2020. "How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk," Journal of Banking & Finance, Elsevier, vol. 111(C).
    5. Joao F. Cocco, 2005. "Portfolio Choice in the Presence of Housing," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 535-567.
    6. Junna Bi & Danping Li, 2023. "Behavioral mean-risk portfolio selection in continuous time via quantile," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(14), pages 4904-4933, July.
    7. Zuo Quan Xu, 2013. "A New Characterization of Comonotonicity and its Application in Behavioral Finance," Papers 1311.6080, arXiv.org, revised Jun 2014.
    8. Haim Levy, 2004. "Prospect Theory and Mean-Variance Analysis," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 1015-1041.
    9. Strobl, Renate, 2022. "Background risk, insurance and investment behaviour: Experimental evidence from Kenya," Journal of Economic Behavior & Organization, Elsevier, vol. 202(C), pages 34-68.
    10. 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..
    11. Li, Jingyuan, 2011. "The demand for a risky asset in the presence of a background risk," Journal of Economic Theory, Elsevier, vol. 146(1), pages 372-391, January.
    12. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    13. Bi, Junna & Jin, Hanqing & Meng, Qingbin, 2018. "Behavioral mean-variance portfolio selection," European Journal of Operational Research, Elsevier, vol. 271(2), pages 644-663.
    14. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    15. Fan, Elliott & Zhao, Ruoyun, 2009. "Health status and portfolio choice: Causality or heterogeneity?," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1079-1088, June.
    16. Francisco J. Gomes, 2005. "Portfolio Choice and Trading Volume with Loss-Averse Investors," The Journal of Business, University of Chicago Press, vol. 78(2), pages 675-706, March.
    17. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2010. "An analysis of portfolio selection with background risk," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3055-3060, December.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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