A general theory of risk apportionment

Christian Gollier ()
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Christian Gollier: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: Stochastic dominance; Risk orders; Prudence; Temperance; Concordance (search for similar items in EconPapers)
Date: 2021
Note: View the original document on HAL open archive server: https://hal.science/hal-04164327v1
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Published in Journal of Economic Theory, 2021, 192, pp.105189. ⟨10.1016/j.jet.2021.105189⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04164327

DOI: 10.1016/j.jet.2021.105189

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