Stochastic Control in Insurance

We outline the structure of stochastic control problems that appear in insurance models. These are classified according to the type of modeling used, the nature of the controls involved, and the objectives, such as ruin probability minimization or dividend optimization. We describe the procedure of the solution via the dynamic programming principle and list the recent advances in this area. Keywords: stochastic control; reinsurance; dynamic programming; Hamilton–Jacobi–Bellman equation; singular control; impulse control