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Concavity, stochastic utility, and risk aversion

Robert Jarrow () and Siguang Li ()
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Siguang Li: Cornell University

Finance and Stochastics, 2021, vol. 25, issue 2, No 4, 330 pages

Abstract: 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.

Keywords: State-dependent utility; Stochastic utility; Risk aversion; Uniform risk aversion; Pointwise concavity; Uniform risk aversion for independent gambles; 91B08; 91B16 (search for similar items in EconPapers)
JEL-codes: D11 D81 G40 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00780-021-00448-5

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