We analyze comparative static effects under uncertainty when a decision maker has mean-variance preferences and faces a generic, quasi-linear decision problem with both an endogenous risk and a background risk. In terms of mean-variance preferences, we fully characterize the effects of changes in the location, scale, and concordance parameters of the stochastic environment on optimal risk taking. Presupposing compatibility between the mean-variance and the expected-utility approach, we then translate these mean-variance properties into their analogues for von Neumann-Morgenstern utility functions.
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Eichner et al. (2009) studied this question.
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