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Concavity, stochastic utility, and risk aversion

Author

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  • Robert Jarrow

    (Cornell University
    Kamakura Corporation)

  • Siguang Li

    (Cornell University)

Abstract

This paper studies the relation between concavity, stochastic or state-dependent utility functions, and risk aversion. Using the common definition of risk aversion, but modified for state-dependent preferences, we show that concavity does not imply risk aversion. Instead, it implies a weaker version of risk aversion, defined herein, and called risk aversion for independent gambles. Furthermore, to characterise the economic meaning of concavity, we define two new risk aversion notions, called uniform risk aversion and uniform risk aversion for independent gambles, respectively. We show that concavity is equivalent to uniform risk aversion for independent gambles, and that concavity plus some additional conditions are equivalent to uniform risk aversion.

Suggested Citation

  • Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:2:d:10.1007_s00780-021-00448-5
    DOI: 10.1007/s00780-021-00448-5
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    More about this item

    Keywords

    State-dependent utility; Stochastic utility; Risk aversion; Uniform risk aversion; Pointwise concavity; Uniform risk aversion for independent gambles;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • G40 - Financial Economics - - Behavioral Finance - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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