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A general theory of risk apportionment

Gollier, Christian (2019) A general theory of risk apportionment. TSE Working Paper, n. 19-1003, Toulouse

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Suppose that the conditional distributions of ˜x (resp. ˜y) can be ranked according to the m-th (resp. n-th) risk order. Increasing their statistical concordance increases the
(m, n) degree riskiness of (˜x, ˜y), i.e., it reduces expected utility for all bivariate utility functions whose sign of the (m, n) cross-derivative is (−1)m+n+1. This means in particular
that this increase in concordance of risks induces a m + n degree risk increase in ˜x + ˜y. On the basis of these general results, I provide different recursive methods to generate
high degrees of univariate and bivariate risk increases. In the reverse-or-translate (resp.reverse-or-spread) univariate procedure, a m degree risk increase is either reversed or
translated downward (resp. spread) with equal probabilities to generate a m + 1 (resp.m + 2) degree risk increase. These results are useful for example in asset pricing theory
when the trend and the volatility of consumption growth are stochastic or statistically linked.

Item Type: Monograph (Working Paper)
Language: English
Date: April 2019
Place of Publication: Toulouse
Uncontrolled Keywords: Stochastic dominance, risk orders, prudence, temperance, concordance.
JEL Classification: D81 - Criteria for Decision-Making under Risk and Uncertainty
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 10 Apr 2019 06:07
Last Modified: 14 Apr 2020 12:16
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