Robust optimal reinsurance-investment problem for $ n $ competitive and cooperative insurers under ambiguity aversion

Abstract

<abstract><p>We investigate a robust optimal reinsurance-investment problem for $ n $ insurers under multiple interactions, which arise from the insurance market, the financial market, the competition mechanism and the cooperation mechanism. Each insurer's surplus process is assumed to follow a diffusion model, which is an approximation of the classical Cramér-Lundberg model. Each insurer is allowed to purchase proportional reinsurance to reduce their claim risk. To reflect the first moment and second moment information on claims, we use the variance premium principle to calculate reinsurance premiums. To increase wealth, each insurer can invest in a financial market, which includes one risk-free asset and $ n $ correlated stocks. Each insurer wants to obtain the robust optimal reinsurance and investment strategy under the mean-variance criterion. By applying a stochastic control technique and dynamic programming approach, the extended Hamilton-Jacobi-Bellman (HJB) equation is established. Furthermore, we derive both the robust optimal reinsurance-investment strategy and the corresponding value function by solving the extended HJB equation. Finally, we present numerical experiments, which yield that competition and cooperation have an important influence on the insurer's decision-making.</p></abstract>