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Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model

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  • Zheng, Xiaoxiao
  • Zhou, Jieming
  • Sun, Zhongyang

Abstract

We investigate a robust optimal portfolio and reinsurance problem under a Cramér–Lundberg risk model for an ambiguity-averse insurer (AAI), who worries about uncertainty in model parameters. Assume that the AAI is allowed to purchase proportional reinsurance and invest his (or her) surplus in a financial market consisting of one risk-free asset and one risky asset whose price is modeled by a constant elasticity of variance (CEV) model. Using techniques of stochastic control, we first derive the closed-form expressions of the optimal strategies and the corresponding value functions for exponential utility function both in the classic compound Poisson risk process and its diffusion approximation, and then the verification theorem is given. Finally, we present numerical examples to illustrate the effects of model parameters on the optimal investment and reinsurance strategies.

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  • 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.
    • Handle: RePEc:eee:insuma:v:67:y:2016:i:c:p:77-87
    DOI: 10.1016/j.insmatheco.2015.12.008
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    Cited by:

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    3. Zhao, Hui & Shen, Yang & Zeng, Yan & Zhang, Wenjun, 2019. "Robust equilibrium excess-of-loss reinsurance and CDS investment strategies for a mean–variance insurer with ambiguity aversion," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 159-180.
    4. Wang, Pei & Li, Zhongfei, 2018. "Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 67-83.
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    6. Zhongyang Sun & Junyi Guo, 2018. "Optimal mean–variance investment and reinsurance problem for an insurer with stochastic volatility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 59-79, August.
    7. 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.
    8. Nicole Bauerle & Gregor Leimcke, 2020. "Robust Optimal Investment and Reinsurance Problems with Learning," Papers 2001.11301, arXiv.org.
    9. Meng, Hui & Liao, Pu & Siu, Tak Kuen, 2019. "Continuous-time optimal reinsurance strategy with nontrivial curved structures," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    11. Zeng, Yan & Li, Danping & Chen, Zheng & Yang, Zhou, 2018. "Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 70-103.
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    13. Zhu, Huainian & Cao, Ming & Zhang, Chengke, 2019. "Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model," Finance Research Letters, Elsevier, vol. 30(C), pages 280-291.
    14. 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.
    15. Yumo Zhang, 2023. "Robust Optimal Investment Strategies for Mean-Variance Asset-Liability Management Under 4/2 Stochastic Volatility Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-32, March.
    16. Li, Danping & Young, Virginia R., 2019. "Optimal reinsurance to minimize the discounted probability of ruin under ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 143-152.
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    20. Zhou Yang & Jing Zhang & Chao Zhou, 2022. "Robust control problems of BSDEs coupled with value functions," Papers 2208.10735, arXiv.org.

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