DISCUSSION PAPERS MAXIMIZING COMPOUND POISSON STOP-LOSS PREMIUMS NUMERICALLY WITH GIVEN MEAN AND VARIANCE

This paper describes a technique to find the maximal stop-loss premiums in a given retention for a compound Poisson risk with known parameter, and known mean and variance of the claims. Restricting to an arithmetic and finite support of the claims, one gets an optimization problem of a non-linear function with a computable gradient, under linear constraints. Numeraical results are given contrasting the method with the method of a previous paper, where only diatomic distributions were considered. 1