IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v42y2008i1p255-260.html
   My bibliography  Save this article

An optimal insurance strategy for an individual under an intertemporal equilibrium

Author

Listed:
  • Zhou, Chunyang
  • Wu, Chongfeng
  • Zhang, Shengping
  • Huang, Xuejun

Abstract

In this paper, we discuss how a risk-averse individual under an intertemporal equilibrium chooses his/her optimal insurance strategy to maximize his/her expected utility of terminal wealth. It is shown that the individual's optimal insurance strategy actually is equivalent to buying a put option, which is written on his/her holding asset with a proper strike price. Since the cost of avoiding risk can be seen as a risk measure, the put option premium can be considered as a reasonable risk measure. Jarrow [Jarrow, R., 2002. Put option premiums and coherent risk measures. Math. Finance 12, 135-142] drew this conclusion with an axiomatic approach, and we verify it by solving the individual's optimal insurance problem.

Suggested Citation

  • Zhou, Chunyang & Wu, Chongfeng & Zhang, Shengping & Huang, Xuejun, 2008. "An optimal insurance strategy for an individual under an intertemporal equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 255-260, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:255-260
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(07)00031-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Promislow, S.David & Young, Virginia R., 2005. "Unifying framework for optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 347-364, June.
    2. Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142, April.
    3. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
    5. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    6. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    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. Zhou, Chunyang & Wu, Chongfeng, 2008. "Optimal insurance under the insurer's risk constraint," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 992-999, June.

    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, LiLi & Wang, Yujin & Shen, Qingjie, 2016. "Optimal reinsurance under VaR and TVaR risk measures in the presence of reinsurer’s risk limit," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 92-100.
    2. Zhou, Chunyang & Wu, Chongfeng, 2008. "Optimal insurance under the insurer's risk constraint," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 992-999, June.
    3. Kaluszka, Marek, 2004. "An extension of Arrow's result on optimality of a stop loss contract," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 527-536, December.
    4. Sun, Wujun & Dong, Dandan, 2015. "On the optimal design of insurance contracts with the restriction of equity risk," Economic Modelling, Elsevier, vol. 51(C), pages 646-652.
    5. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    6. 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.
    7. Sung, K.C.J. & Yam, S.C.P. & Yung, S.P. & Zhou, J.H., 2011. "Behavioral optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 418-428.
    8. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    9. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
    10. Elisa Luciano, 1999. "A Note on Loadings and Deductibles: Can a Vicious Circle Arise?," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1999(2), pages 157-169.
    11. 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.
    12. Giora Harpaz, 1986. "Optimal Risk—Sharing Policies," The American Economist, Sage Publications, vol. 30(2), pages 37-40, October.
    13. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.
    14. Michael Breuer, 2005. "Multiple Losses, EX ANTE Moral Hazard, and the Implications for Umbrella Policies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(4), pages 525-538, December.
    15. Lu, ZhiYi & Liu, LePing & Meng, ShengWang, 2013. "Optimal reinsurance with concave ceded loss functions under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 46-51.
    16. Tridib Bandyopadhyay & Vijay Mookerjee, 0. "A model to analyze the challenge of using cyber insurance," Information Systems Frontiers, Springer, vol. 0, pages 1-25.
    17. Chi, Yichun & Zheng, Jiakun & Zhuang, Shengchao, 2022. "S-shaped narrow framing, skewness and the demand for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 279-292.
    18. Y.M. Ermoliev & S.D. Flam, 2000. "Finding Pareto Optimal Insurance Contracts," Working Papers ir00033, International Institute for Applied Systems Analysis.
    19. Neil A. Doherty & Christian Laux & Alexander Muermann, 2015. "Insuring Nonverifiable Losses," Review of Finance, European Finance Association, vol. 19(1), pages 283-316.
    20. Flåm, Sjur Didrik, 2002. "Full Coverage for Minor, Recurrent Losses?," Working Papers in Economics 10/02, University of Bergen, Department of Economics.

    More about this item

    Statistics

    Access and download statistics

    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:42:y:2008:i:1:p:255-260. 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.