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Optimal Reinsurance and Investment Strategy for an Insurer in a Model with Delay and Jumps

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  • Qiang Zhang

    (Ningxia University)

  • Ping Chen

    (Nanjing University of Science and Technology)

Abstract

This paper studies an optimal excess-of-loss reinsurance and investment problem in a model with delay and jumps for an insurer, who can purchase excess-of-loss reinsurance and invest his surplus in a risk-free asset and a risky asset whose price is governed by a jump-diffusion model. The insurer’s surplus is described by a diffusion model, which is an approximation of the classical compound Poisson risk model. In particular, the wealth process of the insurer is modeled by a stochastic differential delay equation via introducing the performance-related capital inflow or outflow. Under the criterion for maximizing the expected exponential utility of the combination of terminal wealth and average performance wealth, optimal strategy and the corresponding value function are obtained by using the dynamic programming approach. Finally, numerical examples are provided to show the effects of model parameters on the optimal strategies and illustrate the economic meaning.

Suggested Citation

  • Qiang Zhang & Ping Chen, 2020. "Optimal Reinsurance and Investment Strategy for an Insurer in a Model with Delay and Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 777-801, June.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09734-4
    DOI: 10.1007/s11009-019-09734-4
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    References listed on IDEAS

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    1. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    2. A, Chunxiang & Li, Zhongfei, 2015. "Optimal investment and excess-of-loss reinsurance problem with delay for an insurer under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 181-196.
    3. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    4. Xiang Lin & Chunhong Zhang & Tak Siu, 2012. "Stochastic differential portfolio games for an insurer in a jump-diffusion risk process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 83-100, February.
    5. Lihua Bai & Huayue Zhang, 2008. "Dynamic mean-variance problem with constrained risk control for the insurers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 181-205, August.
    6. Jang, Bong-Gyu & Kim, Kyeong Tae, 2015. "Optimal reinsurance and asset allocation under regime switching," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 37-47.
    7. Xiang Lin & Yanfang Li, 2011. "Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(3), pages 417-431.
    8. Gu, Mengdi & Yang, Yipeng & Li, Shoude & Zhang, Jingyi, 2010. "Constant elasticity of variance model for proportional reinsurance and investment strategies," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 580-587, June.
    9. Mou-Hsiung Chang & Tao Pang & Yipeng Yang, 2011. "A Stochastic Portfolio Optimization Model with Bounded Memory," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 604-619, November.
    10. Gu, Ailing & Guo, Xianping & Li, Zhongfei & Zeng, Yan, 2012. "Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 674-684.
    11. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
    12. Zeng, Yan & Li, Danping & Gu, Ailing, 2016. "Robust equilibrium reinsurance-investment strategy for a mean–variance insurer in a model with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 138-152.
    13. Egami, Masahiko & Young, Virginia R., 2009. "Optimal reinsurance strategy under fixed cost and delay," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 1015-1034, March.
    14. 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.
    15. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    16. S. David Promislow & Virginia Young, 2005. "Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 110-128.
    17. 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.
    18. Yi, Bo & Li, Zhongfei & Viens, Frederi G. & Zeng, Yan, 2013. "Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 601-614.
    19. Ya Huang & Xiangqun Yang & Jieming Zhou, 2017. "Robust optimal investment and reinsurance problem for a general insurance company under Heston model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 305-326, April.
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    Cited by:

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    3. Yuan, Yu & Han, Xia & Liang, Zhibin & Yuen, Kam Chuen, 2023. "Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework," European Journal of Operational Research, Elsevier, vol. 311(2), pages 581-595.

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