Robust optimal reinsurance-investment strategy with extrapolative bias premiums and ambiguity aversion

This paper investigates the optimal reinsurance-investment strategy for an insurer whose premium is subject to extrapolative bias. In other words, the insurance premium is dynamically updated by a weighted average of prior claims and the initial estimation of claims. The insurer's surplus follows a diffusion approximation process. He purchases proportional reinsurance or acquires new business to manage insurance risk, and invests his surplus in the financial market, containing a risk-free asset and a risky asset (stock). The price of the risky asset is described by a constant elasticity of variance (CEV) model. The insurer is uncertain about the models of claims and risky asset. In order to derive robust optimal reinsurance-investment strategies, we establish an optimal control problem by maximizing the insurer's expected exponential utility of terminal wealth and solve the optimization problem explicitly. Finally, we present several numerical examples to illustrate our theoretical results.