On cross-risk vulnerability

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• 作者：Y. Malevergne ; B. Rey
• 关键词：Risk aversion ; Risk vulnerability ; Multivariate risk ; Background risk
• 刊名：Insurance: Mathematics and Economics
• 出版年：2009
• 出版时间：October 2009
• 年：2009
• 卷：45
• 期：2
• 页码：224-229
• 全文大小：1188 K

文摘

We introduce the notion of cross-risk vulnerability to generalize the concept of risk vulnerability introduced by Gollier and Pratt [Gollier, C., Pratt, J.W. 1996. Risk vulnerability and the tempering effect of background risk. Econometrica 64, 1109–1124]. While risk vulnerability captures the idea that the presence of an unfair financial background risk should make risk-averse individuals behave in a more risk-averse way with respect to an independent financial risk, cross-risk vulnerability extends this idea to the impact of a non-financial background risk on the financial risk. It provides an answer to the question of the impact of a background risk on the optimal coinsurance rate and on the optimal deductible level. We derive necessary and sufficient conditions for a bivariate utility function to exhibit cross-risk vulnerability both toward an actuarially neutral background risk and toward an unfair background risk. We also analyze the question of the sub-additivity of risk premia and show to what extent cross-risk vulnerability provides an answer.