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Optimal insurance design under background risk with dependence

Author

Listed:
  • Lu, Zhiyi
  • Meng, Shengwang
  • Liu, Leping
  • Han, Ziqi
Abstract
In this paper, we revisit the problem of optimal insurance under a general criterion that preserves stop-loss order when the insured faces two mutually dependent risks: background risk and insurable risk. According to the local monotonicity of conditional survival function, we derive the optimal contract forms in different types of interval. Because the conditional survival function reflects the dependence between background risk and insurable risk, the dependence structure between the two risks plays a critical role in the insured’s optimal insurance design. Furthermore, we obtain the optimal insurance forms explicitly under some special dependence structures. It is shown that deductible insurance is optimal and the Mossin’s Theorem is still valid when background risk is stochastically increasing in insurable risk, which generalizes the corresponding results in Lu et al. (2012). Moreover, we show that an individual will purchase no insurance when the sum of the two risks is stochastically decreasing in insurable risk.

Suggested Citation

  • Lu, Zhiyi & Meng, Shengwang & Liu, Leping & Han, Ziqi, 2018. "Optimal insurance design under background risk with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 15-28.
    • Handle: RePEc:eee:insuma:v:80:y:2018:i:c:p:15-28
    DOI: 10.1016/j.insmatheco.2018.02.006
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    References listed on IDEAS

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    1. Donald J. Meyer & Jack Meyer, 1998. "Changes in Background Risk and the Demand for Insurance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(1), pages 29-40, June.
    2. Mayers, David & Smith, Clifford W, Jr, 1983. "The Interdependence of Individual Portfolio Decisions and the Demand for Insurance," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 304-311, April.
    3. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "The optimal insurance under disappointment theories," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 77-90.
    4. repec:hal:journl:hal-00538974 is not listed on IDEAS
    5. Chi, Yichun & Lin, X. Sheldon, 2014. "Optimal Reinsurance With Limited Ceded Risk: A Stochastic Dominance Approach," ASTIN Bulletin, Cambridge University Press, vol. 44(1), pages 103-126, January.
    6. Carole Bernard & Xuedong He & Jia-An Yan & Xun Yu Zhou, 2015. "Optimal Insurance Design Under Rank-Dependent Expected Utility," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 154-186, January.
    7. Guerra, Manuel & de Lourdes Centeno, Maria, 2008. "Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 529-539, April.
    8. 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.
    9. Meglena Jeleva, 2000. "Background Risk, Demand for Insurance, and Choquet Expected Utility Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 25(1), pages 7-28, June.
    10. Christian Gollier & Harris Schlesinger, 1996. "Arrow's theorem on the optimality of deductibles: A stochastic dominance approach (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 359-363.
    11. Li, Yongwu & Xu, Zuo Quan, 2017. "Optimal insurance design with a bonus," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 111-118.
    12. Guerra, Manuel & Centeno, Maria de Lourdes, 2010. "Optimal Reinsurance for Variance Related Premium Calculation Principles 1," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 97-121, May.
    13. Chi, Yichun & Liu, Fangda, 2017. "Optimal insurance design in the presence of exclusion clauses," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 185-195.
    14. Luigi Guiso & Tullio Jappelli, 1998. "Background Uncertainty and the Demand for Insurance Against Insurable Risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(1), pages 7-27, June.
    15. Doherty, Neil A & Schlesinger, Harris, 1983. "The Optimal Deductible for an Insurance Policy When Initial Wealth Is Random," The Journal of Business, University of Chicago Press, vol. 56(4), pages 555-565, October.
    16. Viala, P. & Briys, E., 1995. "Optimal Insurance Design Under Background Risk," Cahiers de recherche 9550, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    17. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Georges Dionne (ed.), 2013. "Handbook of Insurance," Springer Books, Springer, edition 2, number 978-1-4614-0155-1, February.
    19. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    20. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    21. Soon Koo Hong & Keun Ock Lew & Richard MacMinn & Patrick Brockett, 2011. "Mossin's Theorem Given Random Initial Wealth," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 309-324, June.
    22. Guillaume Carlier & Rose-Anne Dana, 2003. "Pareto efficient insurance contracts when the insurer's cost function is discontinuous," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 871-893, June.
    23. Christian Gollier, 2014. "Optimal insurance design of ambiguous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 555-576, November.
    24. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    25. Elisa Luciano & Robert Kast, 2001. "A Value at Risk Approach to Background Risk," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 26(2), pages 91-115, September.
    26. Edi Karni, 2008. "On Optimal Insurance in the Presence of Moral Hazard*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 33(1), pages 1-18, June.
    27. Mahul, Olivier, 2000. "Optimal insurance design with random initial wealth," Economics Letters, Elsevier, vol. 69(3), pages 353-358, December.
    28. Dana, Rose-Anne & Scarsini, Marco, 2007. "Optimal risk sharing with background risk," Journal of Economic Theory, Elsevier, vol. 133(1), pages 152-176, March.
    29. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
    30. Van Heerwaarden, A. E. & Kaas, R. & Goovaerts, M. J., 1989. "Optimal reinsurance in relation to ordering of risks," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 11-17, March.
    31. repec:dau:papers:123456789/5394 is not listed on IDEAS
    32. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, July.
    33. Chi, Yichun & Tan, Ken Seng, 2011. "Optimal Reinsurance under VaR and CVaR Risk Measures: a Simplified Approach," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 487-509, November.
    34. Olivier Mahul, 2000. "Optimal insurance design with random initial wealth [Contrat optimal d'assurance en présence de risque]," Post-Print hal-02697833, HAL.
    35. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
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