A Stop-Loss Inequality for Compound Poisson Process with a Unimodal Claimsize Distribution

The paper considers the problem of finding an upper bound for the Stop loss premium. We will start with a brief sketch of the practical context in which this problem is relevant. If it is reasonable to assume, that the accumulated claims variable of the underlying risk can be represented by a Compound Poisson Process, the following data are needed for fixing the Stop loss premium: the claims intensity, the distribution of the claim sizes (jump-size variable).