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Approximate utility

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  • Dybvig, Philip H.
  • Li, Shu

Abstract

Approximating arbitrage or a perfect hedge in a limit implies approximation in utility (formally, expected utilities are continuous in L2), if and only if the utility function is bounded above and below by quadratics. We characterize when some special utility functions are continuous for all random consumptions with a common lower bound. Only linear, quadratic, and, in some cases, translated SAHARA utilities are continuous if there is no lower bound. We also characterize when a utility function defined on a convex subset can be extended to an L2-continuous nondecreasing and concave utility function on all of R.

Suggested Citation

  • Dybvig, Philip H. & Li, Shu, 2024. "Approximate utility," Finance Research Letters, Elsevier, vol. 69(PA).
    • Handle: RePEc:eee:finlet:v:69:y:2024:i:pa:s1544612324010729
    DOI: 10.1016/j.frl.2024.106042
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    References listed on IDEAS

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    1. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
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    4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    5. Dybvig, Philip & Liu, Fang, 2018. "On investor preferences and mutual fund separation," Journal of Economic Theory, Elsevier, vol. 174(C), pages 224-260.
    6. 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.
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    More about this item

    Keywords

    Approximate utility; Properness; von Neumann-Morgenstern; Quadratic utility;
    All these keywords.

    JEL classification:

    • G0 - Financial Economics - - General
    • C0 - Mathematical and Quantitative Methods - - General
    • D0 - Microeconomics - - General

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