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Optimal risk sharing with background risk

Author

Listed:
  • Marco Scarsini

    () (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Rose-Anne Dana

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper examines qualitative properties of efficient insurance contracts in the presence of background risk. In order to get results for all strictly risk-averse expected utility maximizers, the concept of “stochastic increasingness” is used. Different assumptions on the stochastic dependence between the insurable and uninsurable risk lead to different qualitative properties of the efficient contracts. The new results obtained under hypotheses of dependent risks are compared to classical results in the absence of background risk or to the case of independent risks. The theory is further generalized to nonexpected utility maximizers.

Suggested Citation

  • Marco Scarsini & Rose-Anne Dana, 2007. "Optimal risk sharing with background risk," Post-Print hal-00538974, HAL.
  • Handle: RePEc:hal:journl:hal-00538974
    DOI: 10.1016/j.jet.2005.10.002
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00538974
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    References listed on IDEAS

    as
    1. Guenter Franke & Richard Stapleton & Marti Subrahmanyam, 2004. "Background risk and the demand for state-contingent claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 321-335, January.
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    Citations

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    Cited by:

    1. Mario Menegatti, 2009. "Optimal saving in the presence of two risks," Journal of Economics, Springer, vol. 96(3), pages 277-288, April.
    2. Biffis, Enrico & Blake, David, 2010. "Securitizing and tranching longevity exposures," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 186-197, February.
    3. Lu, ZhiYi & Liu, LePing & Zhang, JianYu & Meng, LiLi, 2012. "Optimal insurance under multiple sources of risk with positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 462-471.
    4. Damir Filipović & Gregor Svindland, 2008. "Optimal capital and risk allocations for law- and cash-invariant convex functions," Finance and Stochastics, Springer, vol. 12(3), pages 423-439, July.
    5. Ghossoub, Mario, 2015. "Vigilant measures of risk and the demand for contingent claims," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 27-35.
    6. repec:dau:papers:123456789/9738 is not listed on IDEAS
    7. Guenter Franke & Harris Schlesinger & Richard C. Stapleton, 2013. "Risk-Taking-Neutral Background Risk," CESifo Working Paper Series 4070, CESifo Group Munich.
    8. Malamud, Semyon & Rui, Huaxia & Whinston, Andrew, 2016. "Optimal reinsurance with multiple tranches," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 71-82.
    9. repec:eee:insuma:v:77:y:2017:i:c:p:111-118 is not listed on IDEAS
    10. Michail Anthropelos & Gordan Zitkovic, 2008. "On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets," Papers 0803.2198, arXiv.org.
    11. Asimit, Alexandru V. & Badescu, Alexandru M. & Cheung, Ka Chun, 2013. "Optimal reinsurance in the presence of counterparty default risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 690-697.
    12. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    13. Liurui Deng & Traian A. Pirvu, 2016. "Multi-period investment strategies under Cumulative Prospect Theory," Papers 1608.08490, arXiv.org, revised Sep 2017.
    14. repec:eee:insuma:v:76:y:2017:i:c:p:185-195 is not listed on IDEAS
    15. Moshe Levy & Adi Rizansky, 2014. "Market failure in the pharmaceutical industry and how it can be overcome: the CureShare mechanism," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 15(2), pages 143-156, March.
    16. Ekeland Ivar & Schachermayer Walter, 2011. "Law invariant risk measures on L∞ (ℝd)," Statistics & Risk Modeling, De Gruyter, vol. 28(3), pages 195-225, September.
    17. Zuo Quan Xu, 2018. "Quantile optimization under derivative constraint," Papers 1803.02546, arXiv.org.
    18. Ilenia Epifani & Rosella Nicolini, 2013. "On The Population Density Distribution Across Space: A Probabilistic Approach," Journal of Regional Science, Wiley Blackwell, vol. 53(3), pages 481-510, August.
    19. Xu Zuo Quan & Zhou Xun Yu & Zhuang Sheng Chao, 2015. "Optimal Insurance with Rank-Dependent Utility and Increasing Indemnities," Papers 1509.04839, arXiv.org.
    20. Kei Fukuda & Akihiko Inoue & Yumiharu Nakano, 2007. "Optimal intertemporal risk allocation applied to insurance pricing," Papers 0711.1143, arXiv.org, revised Nov 2007.
    21. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
    22. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    23. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.

    More about this item

    Keywords

    Insurance; Efficient contracts; Incomplete markets; Stochastically increasing;

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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