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Optimal Insurance Design Under a Value-at-Risk Framework

Author

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  • Ching-Ping Wang

    (Department of Finance, I-Shou University, No. 1, Section 1, Hsueh-Cheng Rd., Ta-Hsu Hsiang, Kaohsiung County, Taiwan, e-mail: cpwang@isu.edu.tw)

  • David Shyu

    (Department of Finance, National Sun Yat-Sen University, No. 70, Lien-Hai Rd., Kaohsiung, Taiwan, e-mail: dshyu@cm.nsysu.edu.tw)

  • Hung-Hsi Huang

    (Department of Business Administration, Southern Taiwan University of Technology, No. 1, Nan-Tai Street, Yung-Kang, Taiwan, e-mail: d86723002@ntu.edu.tw)

Abstract

This study designs an optimal insurance policy form endogenously, assuming the objective of the insured is to maximize expected final wealth under the Value-at-Risk (VaR) constraint. The optimal insurance policy can be replicated using three options, including a long call option with a small strike price, a short call option with a large strike price, and a short cash-or-nothing call option. Additionally, this study also calculates the optimal insurance levels for these models when we restrict the indemnity to be one of three common forms: a deductible policy, an upper-limit policy, or a policy with proportional coinsurance. The Geneva Risk and Insurance Review (2005) 30, 161–179. doi:10.1007/s10713-005-4677-0

Suggested Citation

  • Ching-Ping Wang & David Shyu & Hung-Hsi Huang, 2005. "Optimal Insurance Design Under a Value-at-Risk Framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 30(2), pages 161-179, December.
    • Handle: RePEc:pal:genrir:v:30:y:2005:i:2:p:161-179
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    Citations

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    Cited by:

    1. Ching-Ping Wang & Hung-Hsi Huang, 2012. "Optimal insurance contract and coverage levels under loss aversion utility preference," Quantitative Finance, Taylor & Francis Journals, vol. 12(10), pages 1615-1628, October.
    2. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    3. Carole Bernard & Weidong Tian, 2009. "Optimal Reinsurance Arrangements Under Tail Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 709-725, September.
    4. Hung-Hsi Huang, 2006. "Optimal insurance contract under a value-at-risk constraint," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(2), pages 91-110, December.
    5. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    6. 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.
    7. Alejandro Drexler & Richard Rosen, 2022. "Exposure to catastrophe risk and use of reinsurance: an empirical evaluation for the U.S," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(1), pages 103-124, January.
    8. Wang, Ching-Ping & Huang, Hung-Hsi, 2016. "Optimal insurance contract under VaR and CVaR constraints," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 110-127.
    9. 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.
    10. Zhang, Lei & Li, Yaoyu, 2017. "Regime-switching based vehicle-to-building operation against electricity price spikes," Energy Economics, Elsevier, vol. 66(C), pages 1-8.
    11. Carole Bernard & Weidong Tian, 2010. "Insurance Market Effects of Risk Management Metrics," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 35(1), pages 47-80, June.
    12. 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.

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