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Optimal Portfolio Under State-Dependent Expected Utility

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  • CAROLE BERNARD

    (Grenoble Ecole de Management, Department of Accounting, Law and Finance, 12 Rue Pierre Sémart, 38000 Grenoble, France†Vrije Universiteit Brussel, Department of Economics and Political Sciences, Pleinlaan 2, 1050 Bruxelles, Belgium)

  • STEVEN VANDUFFEL

    (#x2020;Vrije Universiteit Brussel, Department of Economics and Political Sciences, Pleinlaan 2, 1050 Bruxelles, Belgium)

  • JIANG YE

    (#x2020;Vrije Universiteit Brussel, Department of Economics and Political Sciences, Pleinlaan 2, 1050 Bruxelles, Belgium)

Abstract

We derive the optimal portfolio for an expected utility maximizer whose utility does not only depend on terminal wealth but also on some random benchmark (state-dependent utility). We then apply this result to obtain the optimal portfolio of a loss-averse investor with a random reference point (extending a result of Berkelaar et al. (2004) Optimal portfolio choice under loss aversion, The Review of Economics and Statistics 86 (4), 973–987). Clearly, the optimal portfolio has some joint distribution with the benchmark and we show that it is the cheapest possible in having this distribution. This characterization result allows us to infer the state-dependent utility function that explains the demand for a given (joint) distribution.

Suggested Citation

  • Carole Bernard & Steven Vanduffel & Jiang Ye, 2018. "Optimal Portfolio Under State-Dependent Expected Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-22, May.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:03:n:s0219024918500139
    DOI: 10.1142/S0219024918500139
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    References listed on IDEAS

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    1. 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.
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    8. Steven Vanduffel & Ales Ahcan & Luc Henrard & Mateusz Maj, 2012. "An Explicit Option-Based Strategy That Outperforms Dollar Cost Averaging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-19.
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    Cited by:

    1. Zongxia Liang & Yang Liu & Litian Zhang, 2025. "A framework of state-dependent utility optimisation with general benchmarks," Finance and Stochastics, Springer, vol. 29(2), pages 469-518, April.

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