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Optimal payoffs under state-dependent preferences

Author

Listed:
  • Carole Bernard

    (Journaliste - Revue des ENIL)

  • Franck Moraux

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Ludger Rüschendorf

    (Department of Mathematical Stochastics [Freiburg] - Albert-Ludwigs-Universität Freiburg = University of Freiburg)

  • Steven Vanduffel

    (VUB - Vrije Universiteit Brussel [Bruxelles])

Abstract

Most decision theories, including expected utility theory, rank-dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem.

Suggested Citation

  • Carole Bernard & Franck Moraux & Ludger Rüschendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Post-Print halshs-01118540, HAL.
    • Handle: RePEc:hal:journl:halshs-01118540
    DOI: 10.1080/14697688.2014.981576
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    Cited by:

    1. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2014. "Risk minimization and portfolio diversification," Papers 1411.6657, arXiv.org, revised Dec 2014.
    2. N. Naguez & J. L. Prigent, 2017. "Optimal portfolio positioning within generalized Johnson distributions," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1037-1055, July.
    3. Fajardo, José & Corcuera, José Manuel & Menouken Pamen, Olivier, 2016. "On the optimal investment," MPRA Paper 71901, University Library of Munich, Germany.
    4. Chen, An & Vanduffel, Steven & Wilke, Morten, 2025. "Optimal payoffs under smooth ambiguity," European Journal of Operational Research, Elsevier, vol. 320(3), pages 754-764.
    5. Bernard, Carole & Vanduffel, Steven & Ye, Jiang, 2019. "A new efficiency test for ranking investments: Application to hedge fund performance," Economics Letters, Elsevier, vol. 181(C), pages 203-207.
    6. Xue Dong He & Zhaoli Jiang, 2020. "Optimal Payoff under the Generalized Dual Theory of Choice," Papers 2012.00345, arXiv.org.
    7. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2016. "Risk minimization and portfolio diversification," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1325-1332, September.
    8. Yichun Chi & Zuo Quan Xu & Sheng Chao Zhuang, 2022. "Distributionally Robust Goal-Reaching Optimization in the Presence of Background Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(3), pages 351-382, August.
    9. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.
    10. 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.
    11. Bernard, Carole & Vanduffel, Steven & Ye, Jiang, 2019. "Optimal strategies under Omega ratio," European Journal of Operational Research, Elsevier, vol. 275(2), pages 755-767.
    12. Rüschendorf Ludger & Wolf Viktor, 2015. "Cost-efficiency in multivariate Lévy models," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-16, April.
    13. Carole Bernard & Junsen Tang, 2016. "Simplified Hedge For Path-Dependent Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-32, November.
    14. 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.

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