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Time-consistent mean-variance proportional reinsurance and investment problem in a defaultable market. (English) Zbl 1410.91294

Summary: In this paper, we consider an optimal time-consistent reinsurance-investment problem incorporating a defaultable security for a mean-variance insurer under a constant elasticity of variance (CEV) model. In our model, the insurer’s surplus process is described by a jump-diffusion risk model, the insurer can purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset, a defaultable bond and a risky asset whose price process is assumed to follow a CEV model. Using a game theoretic approach, we establish the extended Hamilton-Jacobi-Bellman system for the post-default case and the pre-default case, respectively. Furthermore, we obtain the closed-from expressions for the time-consistent reinsurance-investment strategy and the corresponding value function in both cases. Finally, we provide numerical examples to illustrate the impacts of model parameters on the optimal time-consistent strategy.

MSC:

91B30 Risk theory, insurance (MSC2010)
93E20 Optimal stochastic control
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