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Optimal payoffs under state-dependent preferences

Author

Listed:
  • Carole Bernard
  • Franck Moraux
  • Ludger Rüschendorf
  • Steven Vanduffel

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," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
  • Handle: RePEc:taf:quantf:v:15:y:2015:i:7:p:1157-1173
    DOI: 10.1080/14697688.2014.981576
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    References listed on IDEAS

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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. repec:taf:quantf:v:17:y:2017:i:7:p:1037-1055 is not listed on IDEAS
    3. Fajardo, José & Corcuera, José Manuel & Menouken Pamen, Olivier, 2016. "On the optimal investment," MPRA Paper 71901, University Library of Munich, Germany.
    4. repec:taf:quantf:v:16:y:2016:i:9:p:1325-1332 is not listed on IDEAS
    5. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.
    6. repec:eee:ejores:v:275:y:2019:i:2:p:755-767 is not listed on IDEAS
    7. Rüschendorf Ludger & Wolf Viktor, 2015. "Cost-efficiency in multivariate Lévy models," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-16, April.
    8. 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.
    9. 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.
    10. repec:wsi:ijtafx:v:21:y:2018:i:03:n:s0219024918500139 is not listed on IDEAS

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