Robust equilibrium reinsurance-investment strategy for a mean–variance insurer in a model with jumps

• Published in: Insurance, mathematics & economics mathematics & economics, 2016-01, Vol.66, p.138-152
• Main Authors: Zeng, Yan, Li, Danping, Gu, Ailing
• Format: Article
• Language: English
• Subjects: Equilibrium; Equilibrium strategy; Investment policy; Jump-diffusion model; Mathematical models; Mean–variance criterion; Reinsurance; Reinsurance and investment; Robust optimal control; Securities markets; Stochastic control theory; Studies
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2015.10.012

This paper analyzes the equilibrium strategy of a robust optimal reinsurance-investment problem under the mean–variance criterion in a model with jumps for an ambiguity-averse insurer (AAI) who worries about model uncertainty. The AAI’s surplus process is assumed to follow the classical Cramér–Lundberg model, and the AAI is allowed to purchase proportional reinsurance or acquire new business and invest in a financial market to manage her risk. The financial market consists of a risk-free asset and a risky asset whose price process is described by a jump-diffusion model. By applying stochastic control theory, we establish the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations. Furthermore, we derive both the robust equilibrium reinsurance-investment strategy and the corresponding equilibrium value function by solving the extended HJB system of equations. In addition, some special cases of our model are provided, which show that our model and results extend some existing ones in the literature. Finally, the economic implications of our findings are illustrated, and utility losses from ignoring model uncertainty, jump risks and prohibiting reinsurance are analyzed using numerical examples. •A new robust mean–variance reinsurance-investment model with jumps is established.•Different ambiguity-averse levels towards diffusion and jump risks are adopted.•The robust equilibrium strategy and corresponding value function are derived.•Some special cases and utility losses from model uncertainty are illustrated.•Some interesting results and phenomena are presented.