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Optimal Investment for an Insurer to Minimize Its Probability of Ruin

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  • Chi Liu
  • Hailiang Yang

Abstract

This paper studies optimal investment strategies of an insurance company. We assume that the insurance company receives premiums at a constant rate, the total claims are modeled by a compound Poisson process, and the insurance company can invest in the money market and in a risky asset such as stocks. This model generalizes the model in Hipp and Plum (2000) by including a risk-free asset. The investment behavior is investigated numerically for various claim-size distributions. The optimal policy and the solution of the associated Hamilton-Jacobi-Bellman equation are then computed under each assumed distribution. Our results provide insights for managers of insurance companies on how to invest. We also investigate the effects of changes in various factors, such as stock volatility, on optimal investment strategies, and survival probability. The model is generalized to cases in which borrowing constraints or reinsurance are present.

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  • 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.
    • Handle: RePEc:taf:uaajxx:v:8:y:2004:i:2:p:11-31
    DOI: 10.1080/10920277.2004.10596134
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    Citations

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    Cited by:

    1. 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.
    2. Xiang Lin, 2009. "Ruin theory for classical risk process that is perturbed by diffusion with risky investments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 33-44, January.
    3. Cao, Jingyi & Landriault, David & Li, Bin, 2020. "Optimal reinsurance-investment strategy for a dynamic contagion claim model," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 206-215.
    4. Zhang, Xin & Siu, Tak Kuen, 2009. "Optimal investment and reinsurance of an insurer with model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 81-88, August.
    5. Bi, Junna & Cai, Jun, 2019. "Optimal investment–reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 1-14.
    6. 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.
    7. Liang, Xiaoqing & Young, Virginia R., 2018. "Minimizing the probability of ruin: Optimal per-loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 181-190.
    8. 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.
    9. 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.
    10. Shen, Yang & Zou, Bin, 2021. "Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 68-80.
    11. Zhao, Hui & Rong, Ximin & Zhao, Yonggan, 2013. "Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 504-514.
    12. Jarraya, Bilel & Bouri, Abdelfettah, 2013. "Multiobjective optimization for the asset allocation of European nonlife insurance companies," MPRA Paper 53697, University Library of Munich, Germany, revised 2013.
    13. Wong, K.C. & Yam, S.C.P. & Zeng, J., 2019. "Mean-risk portfolio management with bankruptcy prohibition," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 153-172.
    14. Hong Mao & Zhongkai Wen, 2020. "Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer with Multi-dimensional Time-Varying Correlation," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(1), pages 29-51, March.
    15. Emms, P. & Haberman, S., 2007. "Asymptotic and numerical analysis of the optimal investment strategy for an insurer," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 113-134, January.
    16. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    17. Arash Fahim & Lingjiong Zhu, 2015. "Optimal Investment in a Dual Risk Model," Papers 1510.04924, arXiv.org, revised Feb 2023.
    18. Guo, Wenjing, 2014. "Optimal portfolio choice for an insurer with loss aversion," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 217-222.
    19. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    20. Qianqian Zhou & Junyi Guo, 2020. "Optimal Control of Investment for an Insurer in Two Currency Markets," Papers 2006.02857, arXiv.org.
    21. 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.
    22. Guan, Guohui & Liang, Zongxia, 2014. "Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 105-115.
    23. Nian Yao & Zhiming Yang, 2017. "Optimal excess-of-loss reinsurance and investment problem for an insurer with default risk under a stochastic volatility model," Papers 1704.08234, arXiv.org.
    24. Mao, Hong & Carson, James M. & Ostaszewski, Krzysztof M. & Wen, Zhongkai, 2013. "Optimal decision on dynamic insurance price and investment portfolio of an insurer," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 359-369.
    25. Zilan Liu & Yijun Wang & Ya Huang & Jieming Zhou, 2022. "Optimal Time-Consistent Investment and Premium Control Strategies for Insurers with Constraint under the Heston Model," Mathematics, MDPI, vol. 10(7), pages 1-22, March.

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