Optimal investment and proportional reinsurance with constrained control variables

In this paper, under the criterion of maximizing the expected exponential utility from terminal wealth, we study the optimal investment and proportional reinsurance strategy for an insurance company. The closed-form expressions for the optimal strategy and value function are derived not only for the compound Poisson risk model but also for the Brownian motion model. We can see that, with normal constraints on the control variables, the value function is still a classical solution to the corresponding Hamilton–Jacobi–Bellman equation.