Concavity, Stochastic Utility, and Risk Aversion

28 Pages Posted: 30 Jan 2020 Last revised: 14 Mar 2021

See all articles by Robert Jarrow

Robert Jarrow

Cornell SC Johnson College of Business

Siguang Li

Cornell University, Dept. of Economics

Date Written: November 17, 2020

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 characterize 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

JEL Classification: D11, G40, D81

Suggested Citation

Jarrow, Robert and Li, Siguang, Concavity, Stochastic Utility, and Risk Aversion (November 17, 2020). Available at SSRN: https://ssrn.com/abstract=3516722 or http://dx.doi.org/10.2139/ssrn.3516722

Robert Jarrow (Contact Author)

Cornell SC Johnson College of Business

Ithaca, NY 14850
United States

Siguang Li

Cornell University, Dept. of Economics ( email )

404 Uris Hall
Ithaca, NY Tompkins 14853
United States

HOME PAGE: http://www.siguangli.com

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