Stability of solutions in optimal reinsurance problem

We consider a discrete-time insurance model with stop-loss reinsurance. One-period insurance claims form a sequence of independent identically distributed nonnegative random variables with finite mean. The insurer maintains the company surplus above a chosen level $a$ by capital injections. We investigate the stability of optimal capital injections to the variability of claims distribution. The term “optimal” means the minimal amount of injections that can be found from the corresponding Bellman equation.