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Optimal investment–reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets

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  • Bi, Junna
  • Cai, Jun

Abstract

In this paper, we investigate the optimal time-consistent investment–reinsurance strategies for an insurer with state dependent risk aversion and Value-at-Risk (VaR) constraints. The insurer can purchase proportional reinsurance to reduce its insurance risks and invest its wealth in a financial market consisting of one risk-free asset and one risky asset, whose price process follows a geometric Brownian motion. The surplus process of the insurer is approximated by a Brownian motion with drift. The two Brownian motions in the insurer’s surplus process and the risky asset’s price process are correlated, which describe the correlation or dependence between the insurance market and the financial market. We introduce the VaR control levels for the insurer to control its loss in investment–reinsurance strategies, which also represent the requirement of regulators on the insurer’s investment behavior. Under the mean–variance criterion, we formulate the optimal investment–reinsurance problem within a game theoretic framework. By using the technique of stochastic control theory and solving the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations, we derive the closed-form expressions of the optimal investment–reinsurance strategies. In addition, we illustrate the optimal investment–reinsurance strategies by numerical examples and discuss the impact of the risk aversion, the correlation between the insurance market and the financial market, and the VaR control levels on the optimal strategies.

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  • 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.
    • Handle: RePEc:eee:insuma:v:85:y:2019:i:c:p:1-14
    DOI: 10.1016/j.insmatheco.2018.11.007
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    References listed on IDEAS

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    3. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2021. "Stochastic differential investment and reinsurance games with nonlinear risk processes and VaR constraints," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 168-184.
    4. Vera Ivanyuk, 2021. "Formulating the Concept of an Investment Strategy Adaptable to Changes in the Market Situation," Economies, MDPI, vol. 9(3), pages 1-19, June.
    5. Hyungbin Park, 2021. "Influence of risk tolerance on long-term investments: A Malliavin calculus approach," Papers 2104.00911, arXiv.org.
    6. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    7. Katia Colaneri & Julia Eisenberg & Benedetta Salterini, 2022. "Some Optimisation Problems in Insurance with a Terminal Distribution Constraint," Papers 2206.04680, arXiv.org.
    8. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Ravanelli, Claudia & Šikić, Mario, 2021. "Revisiting optimal investment strategies of value-maximizing insurance firms," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 131-151.
    9. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    10. Jingtang Ma & Zhengyang Lu & Zhenyu Cui, 2022. "Delta family approach for the stochastic control problems of utility maximization," Papers 2202.12745, arXiv.org.

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