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Optimal investment, consumption and proportional reinsurance for an insurer with option type payoff

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  • Peng, Xingchun
  • Wei, Linxiao
  • Hu, Yijun

Abstract

This paper is devoted to the study of optimization of investment, consumption and proportional reinsurance for an insurer with option type payoff at the terminal time under the criterion of exponential utility maximization. The surplus process of the insurer and the financial risky asset process are assumed to be diffusion processes driven by Brownian motions which are non-Markovian in general. Very general constraints are imposed on the investment and the proportional reinsurance processes. Based on the martingale optimization principle, we use BSDE and BMO martingale techniques to derive the optimal strategy and the optimal value function. Some interesting particular cases are studied in which the explicit expressions for the optimal strategy are given by using the Malliavin calculus.

Suggested Citation

  • Peng, Xingchun & Wei, Linxiao & Hu, Yijun, 2014. "Optimal investment, consumption and proportional reinsurance for an insurer with option type payoff," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 78-86.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:78-86
    DOI: 10.1016/j.insmatheco.2014.09.002
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    References listed on IDEAS

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    1. Zhang, Xin-Li & Zhang, Ke-Cun & Yu, Xing-Jiang, 2009. "Optimal proportional reinsurance and investment with transaction costs, I: Maximizing the terminal wealth," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 473-478, June.
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    3. Peng, Xingchun & Hu, Yijun, 2013. "Optimal proportional reinsurance and investment under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 416-428.
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    Cited by:

    1. Peng, Xingchun & Wang, Wenyuan, 2016. "Optimal investment and risk control for an insurer under inside information," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 104-116.
    2. Zhao, Qian & Wang, Rongming & Wei, Jiaqin, 2016. "Exponential utility maximization for an insurer with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 89-104.
    3. Martin Eling & Ruo Jia, 2017. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 20(1), pages 63-77, March.
    4. Peng, Xingchun & Chen, Fenge & Wang, Wenyuan, 2021. "Robust optimal investment and reinsurance for an insurer with inside information," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 15-30.
    5. Xue, Xiaole & Wei, Pengyu & Weng, Chengguo, 2019. "Derivatives trading for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 40-53.

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