Working paper

Variance stochastic orders

Christian Gollier

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.

Keywords

Long-run risk; stochastic dominance; prudence; temperance; stochastic volatility; risk apportionment;

JEL codes

  • D81: Criteria for Decision-Making under Risk and Uncertainty

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.

See also

Published in

TSE Working Paper, n. 17-828, July 2017