IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v51y2012i2p462-471.html
   My bibliography  Save this article

Optimal insurance under multiple sources of risk with positive dependence

Author

Listed:
  • Lu, ZhiYi
  • Liu, LePing
  • Zhang, JianYu
  • Meng, LiLi

Abstract

In this paper we try to derive an optimal insurance treaty when the insured faces multiple sources of risk. We show that the deductible insurance is optimal when the insurable and uninsurable risks are positively dependent or independent within the expected utility framework. A necessary condition of optimal deductible is given under some mild conditions. We compare our model with the classical one without background risk. Furthermore, the shifts of optimal deductible and expected utility by modifications of the dependence structure and the marginal are analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:462-471
    DOI: 10.1016/j.insmatheco.2012.06.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000789
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2012.06.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    3. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    4. 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.
    5. Kischka, Peter, 1988. "Aspects of optimal insurance demand when there are uninsurable risks," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 9-14, January.
    6. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    7. repec:hal:journl:hal-00538974 is not listed on IDEAS
    8. Dana, Rose-Anne & Scarsini, Marco, 2007. "Optimal risk sharing with background risk," Journal of Economic Theory, Elsevier, vol. 133(1), pages 152-176, March.
    9. 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.
    10. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Liu, Ying & Li, Xiaozhong & Liu, Yinli, 2015. "The bounds of premium and optimality of stop loss insurance under uncertain random environments," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 273-278.
    3. 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.
    4. Yichun Chi & Wei Wei, 2020. "Optimal insurance with background risk: An analysis of general dependence structures," Finance and Stochastics, Springer, vol. 24(4), pages 903-937, October.
    5. Hong Liang, 2020. "On Three Standard Results in the Theory of Insurance Demand," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(1), pages 1-10, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Yichun Chi & Wei Wei, 2020. "Optimal insurance with background risk: An analysis of general dependence structures," Finance and Stochastics, Springer, vol. 24(4), pages 903-937, October.
    3. Sebastian Hinck & Petra Steinorth, 2023. "Insurance demand in the presence of loss‐dependent background risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(4), pages 991-1026, December.
    4. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    5. Jianli Wang & Yingrong Su & Jingyuan Li & Ho Yin Yick, 2022. "Demand for insurance with nonadditive probabilistic beliefs," Bulletin of Economic Research, Wiley Blackwell, vol. 74(3), pages 854-862, July.
    6. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    7. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    8. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    9. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    10. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
    11. Henri Loubergé, 1998. "Risk and Insurance Economics 25 Years After," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 23(4), pages 540-567, October.
    12. Reichel, Lukas & Schmeiser, Hato & Schreiber, Florian, 2021. "Sometimes more, sometimes less: Prudence and the diversification of risky insurance coverage," European Journal of Operational Research, Elsevier, vol. 292(2), pages 770-783.
    13. Donald C., Rudow, 2005. "Preferences and Increased Risk Aversion under a General Framework of Stochastic Dominance," MPRA Paper 41191, University Library of Munich, Germany, revised 07 Jun 2005.
    14. repec:dau:papers:123456789/698 is not listed on IDEAS
    15. 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.
    16. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    17. Udo Broll & Peter Welzel & Kit Wong, 2015. "Futures hedging with basis risk and expectation dependence," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 62(3), pages 213-221, September.
    18. 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.
    19. Arthur Hau, 1999. "A Note on Insurance Coverage in Incomplete Markets," Southern Economic Journal, John Wiley & Sons, vol. 66(2), pages 433-441, October.
    20. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    21. Liang, Xiaoqing & Young, Virginia R., 2018. "Minimizing the probability of ruin: Optimal per-loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 181-190.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:462-471. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.