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Variance Vulnerability, Background Risks, and Mean-Variance Preferences

Thomas Eichner and Andreas Wagener
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Thomas Eichner: VWL IV, FB 5, University of Siegen, Hölderlinstr. 3, 57068 Siegen, Germany, e-mail:

The Geneva Risk and Insurance Review, 2003, vol. 28, issue 2, 173-184

Abstract: An agent with two-parameter, mean-variance preferences is called variance vulnerable if an increase in the variance of an exogenous, independent background risk induces the agent to choose a lower level of risky activities. Variance vulnerability resembles the notion of risk vulnerability in the expected utility (EU) framework. First, we characterize variance vulnerability in terms of two-parameter utility functions. Second, we identify the multivariate normal as the only distribution such that EU- and two-parameter approach are compatible when independent background risks prevail. Third, presupposing normality, we show that—analogously to risk vulnerability—temperance is a necessary, and standardness and convex risk aversion are sufficient conditions for variance vulnerability. The Geneva Papers on Risk and Insurance Theory (2003) 28, 173–184. doi:10.1023/A:1026396922206

Date: 2003
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