A general theory of risk apportionment

Abstract

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.

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Replaced by

Christian Gollier, “A general theory of risk apportionment”, Journal of Economic Theory, vol. 192, n. 105189, March 2021.

Reference

Christian Gollier, “A general theory of risk apportionment”, TSE Working Paper, n. 19-1003, April 2019.