Optimal investment and reinsurance strategies with federal income tax under the Geometric Mean Reversion (GMR) model

This paper considered optimal investment and reinsurance strategies under the Geometric Mean Reversion (GMR) model when the insurer pays Federal income tax on the dividends. A Brownian motion with drift is used for modeling the insurer's surplus process. The financial market consists of one risk-free asset and one risky asset whose price process satisfies the Geometric Mean Reversion (GMR) model. The objective of the insurer is to maximize the utility of terminal wealth. In the framework of stochastic control, explicit expressions for optimal strategies are derived. In addition, a number of intriguing results are obtained, and numerical simulations are presented to demonstrate our findings.