Variance stochastic orders

Abstract

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.

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JEL codes

Replaced by

Christian Gollier, “Variance stochastic orders”, Journal of Mathematical Economics, vol. 80, January 2019, pp. 1–8.

Reference

Christian Gollier, “Variance stochastic orders”, TSE Working Paper, n. 17-828, July 2017.