Optimizing Insurance and Reinsurance in the Dynamic Cramer–Lundberg Model
We find optimal (from the insurer’s point of view) strategies for insurance and reinsurance
in a controllable Cramer–Lundberg risk process that describes the capital dynamics of
an insurance company over an infinite 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 deductible. Equations that define optimal strategies parameters are derived.