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Optimal investment for an insurer in the Lévy market: The martingale approach

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  • Zhou, Qing

Abstract

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to study the optimal investment problem for an insurer. When the risk and security assets are described by the Lévy processes and utility is CARA, the closed-form solutions to the maximization problem are obtained.

Suggested Citation

  • Zhou, Qing, 2009. "Optimal investment for an insurer in the Lévy market: The martingale approach," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1602-1607, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:14:p:1602-1607
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    References listed on IDEAS

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    1. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    2. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    3. Chi Liu & Hailiang Yang, 2004. "Optimal Investment for an Insurer to Minimize Its Probability of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(2), pages 11-31.
    4. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    5. Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
    6. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    7. Wang, Nan, 2007. "Optimal investment for an insurer with exponential utility preference," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 77-84, January.
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    Cited by:

    1. Ryle S. Perera & Kimitoshi Sato, 2018. "Optimal asset allocation for a bank under risk control," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-27, September.
    2. Perera, Ryle S., 2010. "Optimal consumption, investment and insurance with insurable risk for an investor in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 479-484, June.
    3. Zhou, Jieming & Yang, Xiangqun & Guo, Junyi, 2017. "Portfolio selection and risk control for an insurer in the Lévy market under mean–variance criterion," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 139-149.
    4. Rafael Serrano & Camilo Castillo, 2018. "ALM for insurers with multiple underwriting lines and portfolio constraints: a Lagrangian duality approach," Papers 1810.08466, arXiv.org, revised Aug 2021.

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