Optimal non-proportional reinsurance control

This paper deals with the problem of ruin probability minimization under various investment control and reinsurance schemes. We first look at the minimization of ruin probabilities in the models in which the surplus process is a continuous diffusion process in which we employ stochastic control to find the optimal policies for reinsurance and investment. We then focus on the case in which the surplus process is modeled via a classical Lundberg process, i.e. the claims process is compound Poisson. There, the optimal reinsurance policy is derived from the Hamilton–Jacobi–Bellman equation.