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Modeling non-monotone risk aversion using SAHARA utility functions

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  • Chen, An
  • Pelsser, Antoon
  • Vellekoop, Michel

Abstract

We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under SAHARA utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how SAHARA utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.

Suggested Citation

  • Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, September.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:2075-2092
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    11. Chen, Dengsheng & Lu, Zhengyang & He, Yong, 2023. "Optimal reinsurance-investment game for two insurers with SAHARA utilities under correlated markets," The North American Journal of Economics and Finance, Elsevier, vol. 68(C).
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    13. Dybvig, Philip H. & Li, Shu, 2024. "Approximate utility," Finance Research Letters, Elsevier, vol. 69(PA).
    14. Matteo Brachetta & Hanspeter Schmidli, 2019. "Optimal Reinsurance and Investment in a Diffusion Model," Papers 1903.12426, arXiv.org.
    15. Taras Bodnar & Dmytro Ivasiuk & Nestor Parolya & Wofgang Schmid, 2018. "Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios," Papers 1806.08005, arXiv.org, revised May 2019.
    16. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.
    17. Fernando Alvarez, 2018. "A three mutual fund separation theorem," 2018 Meeting Papers 1066, Society for Economic Dynamics.
    18. Cui, Zhenyu, 2014. "Comment on “Modeling non-monotone risk aversion using SAHARA utility functions” [J. Econ. Theory 146 (2011) 2075–2092]," Journal of Economic Theory, Elsevier, vol. 153(C), pages 703-705.
    19. Christian Laudag'e & Felix-Benedikt Liebrich, 2025. "When risk defies order: On the limits of fractional stochastic dominance," Papers 2509.24747, arXiv.org.
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    21. Fagart, Marie-Cécile & Fluet, Claude, 2013. "The first-order approach when the cost of effort is money," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 7-16.
    22. Chen, An & Hieber, Peter & Nguyen, Thai, 2019. "Constrained non-concave utility maximization: An application to life insurance contracts with guarantees," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1119-1135.
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    24. Jaap Spreeuw, 2022. "The Copula Derived from the SAHARA Utility Function," Risks, MDPI, vol. 10(7), pages 1-10, June.
    25. Nicole Bauerle & An Chen, 2022. "Optimal investment under partial information and robust VaR-type constraint," Papers 2212.04394, arXiv.org, revised Sep 2023.

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