Time-consistent mean–variance proportional reinsurance and investment problem in a defaultable market. (4th May 2018)

• Record Type: Journal Article
• Authors: Zhang, Qiang; Chen, Ping
• Is Part Of: Optimization. Volume 67:Number 5(2018)
• Page Start: 683
• Page End: 699
• Publication Date: 2018-05-04
• Subjects: Time-consistent strategy -- mean–variance -- CEV model -- defaultable bond -- proportional reinsurance; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1434650
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: 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.