Optimal reinsurance and investment problem with the minimum capital deposit constraint

This paper studies the optimal reinsurance and investment problem of the insurance company. During the optimization phase, the existence of capital deposit requires that the insurer's wealth should be above the given minimum value. The aim is to minimize the distance between the wealth and the given target at the terminal time. We first convert the value function's domain to a rectangle and then derive the Hamilton-Jacobi-Bellman equation via the dynamic programming principle. By solving the explicit solutions for the Hamilton-Jacobi-Bellman equation, we obtain the expression of the optimal reinsurance and investment policy. In the last, several examples are presented to illustrate the sensitivity analysis of different parameters.