Time-consistent robust investment-reinsurance strategy with common shock dependence under CEV model

Abstract

This paper investigates the optimal robust equilibrium investment and reinsurance strategy in a model with common shock dependent claims for an ambiguity-averse insurer (AAI). Suppose that the insurance company can purchase proportional reinsurance whose reinsurance premium is calculated by the expected value principle to disperse risks. The ambiguity-averse insurer’s wealth process have two dependent classes of insurance business and the surplus can be invested in a financial market composed of one risk-free asset and one risky asset, where the risky asset’s price is characterized by the constant elasticity of variance (CEV) model. Applying the game theory framework under the mean-variance criterion, the optimal investment reinsurance problem are derived. By adopting stochastic control theory and solving the corresponding extended Hamilton-Jacobi-Bellman (HJB) equations, we obtain the robust optimal investment-reinsurance strategy and the corresponding equilibrium value function. Furthermore, some numerical examples are provided to illustrate the effects of model parameters on the optimal investment and reinsurance strategy.