Optimal reinsurance in the model with several risks within one insurance policy

We study the model of insurance company performance that issues insurance policies covering several risks. Each risk can be reinsured according to the arbitrary reinsurance treaty. Parameters of such reinsurance treaties can be changed dynamically. The main aim is to find an optimal reinsurance strategy that maximises the probability of survival of the insurance company. The Hamilton–Jacobi–Bellman equation for this problem is deduced and existence and uniqueness of its solution are proved. We also establish the optimal reinsurance strategy and give numerical results for the special case of claim distribution.