Broadly Decreasing Risk Aversion

Gregory M. Gelles · Douglas W. Mitchell

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Decision-Making and Behavioral Economics Capital Investment and Risk Analysis Risk and Portfolio Optimization

Abstract

This paper considers decision-making in the presence of two additive risk sources, with no restrictions on the relation between the two risks. A utility function is said to exhibit broad DARA if and only if a rise in wealth always decreases the magnitude of the risk premium for one of the risks vis-a-vis the other. A condition on utility functions giving this property is derived: utility must be of the linear plus exponential form. It is shown that certain problems involving portfolios and risk-averse firms give unambiguous comparative statics if and only if utility exhibits broad DARA.

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References

1964Risk Aversion in the Small and in the Large 1976Risk Aversion in the Small and in the Large 1966Aspects of the Theory of Risk-Bearing.1990Precautionary Saving in the Small and in the Large 1989Precautionary Saving in the Small and in the Large 1971On the theory of the competitive firm under price uncertainty 1996Risk Vulnerability and the Tempering Effect of Background Risk 1981Some Stronger Measures of Risk Aversion in the Small and the Large with Applications

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2012Ross risk vulnerability for introductions and changes in background risk 2007Generalised Means of Simple Utility Functions with Risk Aversion 2014Risk‐Sensitive Multiagent Decision‐Theoretic Planning Based on MDP and One‐Switch Utility Functions

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