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On Cross-risk Vulnerability

Author

Listed:
  • Yannick Malevergne

    (COACTIS - COnception de l'ACTIon en Situation - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne)

  • Béatrice Rey

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract
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.

Suggested Citation

  • Yannick Malevergne & Béatrice Rey, 2009. "On Cross-risk Vulnerability," Post-Print halshs-00520050, HAL.
    • Handle: RePEc:hal:journl:halshs-00520050
    DOI: 10.1016/j.insmatheco.2009.06.002
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00520050
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    Cited by:

    1. Björn Bos & Moritz A. Drupp & Jasper N. Meya & Martin F. Quaas, 2023. "Financial Risk-Taking under Health Risk," CESifo Working Paper Series 10387, CESifo.
    2. Crainich, David & Eeckhoudt, Louis & Le Courtois, Olivier, 2017. "Health and portfolio choices: A diffidence approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 273-279.
    3. Christophe Courbage & Guillem Montoliu-Montes & Béatrice Rey, 2018. "How vulnerable is risk aversion to wealth, health and other risks? An empirical analysis for Europe," Working Papers halshs-01935846, HAL.
    4. Christophe Courbage & Guillem Montoliu-Montes & Béatrice Rey, 2018. "How vulnerable is risk aversion to wealth, health and other risks? An empirical analysis for Europe," Working Papers 1827, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    5. David Crainich & Louis Eeckhoudt & Olivier Le Courtois, 2013. "An index of (absolute) correlation aversion: theory and some implications," Working Papers 2013-ECO-12, IESEG School of Management.
    6. Lu Li & Andreas Richter & Petra Steinorth, 2023. "Mental health changes and the willingness to take risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 48(1), pages 31-62, March.
    7. Stefani Milovanska-Farrington & Stephen Farrington, 2021. "Discipline, risk, and the endogeneity between financial decisionmaking and health," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 45(4), pages 596-636, October.

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