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On Cross-risk Vulnerability

  • Yannick Malevergne

    ()

    (COACTIS - Université Lumière - Lyon II : EA4161 - Université Jean Monnet - Saint-Etienne)

  • Rey Beatrice

    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

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.

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Paper provided by HAL in its series Post-Print with number halshs-00520050.

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Date of creation: 01 Oct 2009
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Publication status: Published, Insurance: Mathematics and Economics, 2009, 45, 2, 224-229
Handle: RePEc:hal:journl:halshs-00520050
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00520050/en/
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