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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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Suggested Citation

  • Fanny Demers & Michel Demers, 1991. "Multivariate Risk Aversion and Uninsurable Risks: Theory and Applications," Carleton Economic Papers 91-04, Carleton University, Department of Economics, revised Jun 1991.
  • Handle: RePEc:car:carecp:91-04

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    Cited by:

    1. Huang, Hung-Hsi & Wang, Ching-Ping, 2013. "Portfolio selection and portfolio frontier with background risk," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 177-196.
    2. Courbage, Christophe, 1999. "Primes de risque et soins de santé," L'Actualité Economique, Société Canadienne de Science Economique, vol. 75(4), pages 665-672, décembre.
    3. Christophe Courbage, 2014. "Saving motives and multivariate precautionary premia," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 385-391, October.
    4. Christophe Courbage, 2001. "On Bivariate Risk Premia," Theory and Decision, Springer, vol. 50(1), pages 29-34, February.

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    risk; insurance; economic models;


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