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Upper bound for ruin probabilities under optimal investment and proportional reinsurance

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  • Zhibin Liang
  • Junyi Guo

Abstract

In this paper, we consider the optimal investment and reinsurance from an insurer's point of view to maximize the adjustment coefficient. We obtain the explicit expressions for the optimal results in the diffusion approximation (D‐A) case as well as in the jump‐diffusion (J‐D) case. Furthermore, we derive a sharper bound on the ruin probability, from which we conclude that the case with investment is always better than the case without investment. Some numerical examples are presented to show that the ruin probability in the D‐A case sometimes underestimates the ruin probability in the J‐D case. Copyright © 2007 John Wiley & Sons, Ltd.

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  • Zhibin Liang & Junyi Guo, 2008. "Upper bound for ruin probabilities under optimal investment and proportional reinsurance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(2), pages 109-128, March.
    • Handle: RePEc:wly:apsmbi:v:24:y:2008:i:2:p:109-128
    DOI: 10.1002/asmb.694
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    Cited by:

    1. Yuen, Kam Chuen & Liang, Zhibin & Zhou, Ming, 2015. "Optimal proportional reinsurance with common shock dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 1-13.
    2. Caibin Zhang & Zhibin Liang & Kam Chuen Yuen, 2019. "Optimal dynamic reinsurance with common shock dependence and state-dependent risk aversion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-45, March.
    3. Liang, Zhibin & Yuen, Kam Chuen & Guo, Junyi, 2011. "Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 207-215, September.
    4. Xiang Hu & Lianzeng Zhang, 2016. "Ruin Probability in a Correlated Aggregate Claims Model with Common Poisson Shocks: Application to Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 675-689, September.
    5. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    6. Liang, Xiaoqing & Liang, Zhibin & Young, Virginia R., 2020. "Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 128-146.
    7. Guan, Guohui & Liang, Zongxia, 2019. "Robust optimal reinsurance and investment strategies for an AAI with multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 63-78.
    8. Meng, Hui & Wei, Li & Zhou, Ming, 2023. "Multiple per-claim reinsurance based on maximizing the Lundberg exponent," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 33-47.

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