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Multivariate Risk Aversion and Uninsurable Risks: Theory and Applications

The objective of this paper is to develop conditions for global multivariate comparative risk aversion in the presence of uninsurable, or background, risks, and thus generalize Kihlstrom and Mirman [1974] and Karni [1979, 1989]. We analyze von Neumann-Morgenstern (VNM) utility functionsas well as smooth preference functionals which are nonlinear in distribution but locally linear in probabilities. In each case we provide an economic application which illustrates how our theorems can be used. We analyze a risk sharing, a portfolio choice, and a labor supply problem for VNM utility functions, and the optimal allocation of effort to risky technologies in the presence of a random supply (or quality) of a public good for nonlinear preference functionals. We consider thecase where the random variables are mean-independent as well as the case where they are independent. In the labor supply application for VNM utility functions, we show that if the two risks are independent, the comparative statics effect of greater risk aversion on labor supply in the presence of a background non-wage income risk is determined by a monotonic relationship between labor supply and the wage rate under certainty. That is, we extend the applicability of the Diamond-Stiglitz [1974]-Kihlstrom-Mirman [1974] single-crossing property to the case where an independent background risk is present. The Geneva Papers on Risk and Insurance Theory (1991) 16, 7–43. doi:10.1007/BF00942855

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Paper provided by Carleton University, Department of Economics in its series Carleton Economic Papers with number 91-04.

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Length: 37 pages
Date of creation: 1991
Date of revision: Jun 1991
Publication status: Published: – revised version in Geneva Papers on Risk and Insurance Theory, Vol. 16, No. 1 (June 1991), pp. 7–43
Handle: RePEc:car:carecp:91-04
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