A general theory of risk apportionment

• 成果类型: Article
• 署名作者: Gollier, Christian
• 署名单位: Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2021.105189
• 发表日期: 2021
• 关键词: Stochastic dominance; Risk orders; prudence; Temperance; CONCORDANCE

摘要

Suppose that the conditional distributions of (x) over tilde (resp. (y) over tilde) 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) over tilde, (y) over tilde), 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) over tilde + (y) over tilde. 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. (C) 2021 Elsevier Inc. All rights reserved.