Optimizing insurance and reinsurance in the dynamic Cramér–Lundberg model

We find optimal (from the insurer's point of view) strategies for insurance and reinsurance in a controllable Cramér–Lundberg risk process that describes the capital dynamics of an insurance company over an extended time interval. As the optimality criterion being minimized, we use the stationary variation coefficient, taking into account additional constraints on residual risks for both insurers and reinsurer. We establish that it is best to use stop-loss reinsurance with an upper limit and insurance which is a combination of a stop-loss strategy and franchise. We derive equations that define optimal strategy parameters.