Variance stochastic orders

Gollier, Christian (2017) Variance stochastic orders. TSE Working Paper, n. 17-828, Toulouse

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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.

Item Type: Monograph (Working Paper)
Language: English
Date: July 2017
Place of Publication: Toulouse
Uncontrolled Keywords: Long-run risk, stochastic dominance, prudence, temperance, stochastic volatility, risk apportionment
JEL codes: D81 - Criteria for Decision-Making under Risk and Uncertainty
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 14 Mar 2018 13:44
Last Modified: 20 Nov 2018 13:04

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