OPTIMAL INVESTMENT AND REINSURANCE WITH PREMIUM CONTROL

Abstract

abstract. This paper studies the optimal investment and reinsurance prob-lem for a risk model with premium control. It is assumed that the insurance safety loading and the time-varying claim arrival rate are connected through a monotone decreasing function, and that the insurance and reinsurance safety loadings have a linear relationship. Applying stochastic control theory, we are able to derive the optimal strategy that maximizes the expected exponential utility of terminal wealth. We also provide a few numerical examples to illus-trate the impact of the model parameters on the optimal strategy.