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Article Dans Une Revue Journal of Economic Theory Année : 2021

A general theory of risk apportionment

Christian Gollier
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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.
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Dates et versions

hal-04164327 , version 1 (18-07-2023)

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Christian Gollier. A general theory of risk apportionment. Journal of Economic Theory, 2021, 192, pp.105189. ⟨10.1016/j.jet.2021.105189⟩. ⟨hal-04164327⟩
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