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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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    3. Chen, An & Hieber, Peter & Sureth, Caren, 2022. "Pay for tax certainty? Advance tax rulings for risky investment under multi-dimensional tax uncertainty," arqus Discussion Papers in Quantitative Tax Research 273, arqus - Arbeitskreis Quantitative Steuerlehre.
    4. Zongxia Liang & Yang Liu & Ming Ma & Rahul Pothi Vinoth, 2021. "A Unified Formula of the Optimal Portfolio for Piecewise Hyperbolic Absolute Risk Aversion Utilities," Papers 2107.06460, arXiv.org, revised Oct 2023.
    5. 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.
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    7. Moris S. Strub & Xun Yu Zhou, 2021. "Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes," Finance and Stochastics, Springer, vol. 25(2), pages 331-358, April.
    8. Panagiotis E. Souganidis & Thaleia Zariphopoulou, 2024. "Mean field games with unbounded controlled common noise in portfolio management with relative performance criteria," Mathematics and Financial Economics, Springer, volume 18, number 10, December.
    9. Bernard, Carole & De Gennaro Aquino, Luca & Levante, Lucia, 2021. "Optimal annuity demand for general expected utility agents," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 70-79.
    10. Marcellino Gaudenzi & Michel Vellekoop, 2018. "Exact Solutions for Optimal Investment Strategies and Indifference Prices under Non-Differentiable Preferences," Papers 1809.11010, arXiv.org.
    11. Dybvig, Philip & Liu, Fang, 2018. "On investor preferences and mutual fund separation," Journal of Economic Theory, Elsevier, vol. 174(C), pages 224-260.
    12. Yang Liu & Zhenyu Shen, 2024. "PSAHARA Utility Family: Modeling Non-monotone Risk Aversion and Convex Compensation in Incomplete Markets," Papers 2406.00435, arXiv.org, revised Nov 2024.
    13. Matteo Brachetta & Hanspeter Schmidli, 2019. "Optimal Reinsurance and Investment in a Diffusion Model," Papers 1903.12426, arXiv.org.
    14. 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.
    15. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.
    16. Fernando Alvarez, 2018. "A three mutual fund separation theorem," 2018 Meeting Papers 1066, Society for Economic Dynamics.
    17. 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.
    18. 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.
    19. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    20. Jaap Spreeuw, 2022. "The Copula Derived from the SAHARA Utility Function," Risks, MDPI, vol. 10(7), pages 1-10, June.
    21. 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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