Document de travail

A general theory of risk apportionment

Christian Gollier

Résumé

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.

Mots-clés

Stochastic dominance; risk orders; prudence; temperance; concordance.;

Codes JEL

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

Remplacé par

Christian Gollier, « A general theory of risk apportionment », Journal of Economic Theory, vol. 192, n° 105189, mars 2021.

Référence

Christian Gollier, « A general theory of risk apportionment », TSE Working Paper, n° 19-1003, avril 2019.

Voir aussi

Publié dans

TSE Working Paper, n° 19-1003, avril 2019