Bounds for stop-loss premium under restrictions on I-divergence

Stop-loss reinsurance contracts have attracted much attention recently. In its simplest form, the reinsurer agrees to pay all losses of the insurer in excess of an agreed-upon limit. This paper concerns the calculation of upper and lower bounds on the stop-loss premium, i.e. the expected payment by the reinsurer, when the claim distribution is unknown but assumed to be in the proximity (as measured by I-divergence) of the empirical distribution of past claims. The problems of computing the upper and lower bounds on the premium are modeled as nonlinear constrained optimization problems, namely, generalized geometric programs. Simple solution procedures, based upon generalized geometric programming duality, are described and demonstrated for an example.