%0 Report
%9 Working Paper
%A Gollier, Christian
%B TSE Working Paper
%C Toulouse
%D 2017
%F publications:24198
%I Université Toulouse 1 Capitole
%K Long-run risk
%K stochastic dominance
%K prudence
%K temperance
%K stochastic volatility
%K risk apportionment
%T Variance stochastic orders
%U https://publications.ut-capitole.fr/id/eprint/24198/
%V 17-828
%X Suppose that the decision-maker is uncertain about the variance of the payoff of a gamble, and that this uncertainty comes from not knowing the number of zero-mean i.i.d. risks attached to the gamble. In this context, we show that any n-th degree increase in this variance risk reduces expected utility if and only if the sign of the 2n-th derivative of the utility function u is (-1)n+1. Moreover, increasing the statistical concordance between the mean payoff of the gamble and the n-th degree riskiness of its variance reduces expected utility if and only if the sign of the 2n + 1 derivative of u is (-1)n+1. These results generalize the theory of risk apportionment developed by Eeckhoudt and Schlesinger (2006), and is useful to better understand the impact of stochastic volatility on welfare and asset prices.