Exponential estimates for the stop-loss premium

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Abstract
This paper analyses the stop-loss premium II(c, t) for the standard risk model in which the number of claims in (0, t] is Poisson with intensity 1 and the claimsize distribution F is on (-∞, +∞) with mean µ>0. It is shown that, under typical conditions on F, II(c, t)=µt-c+R(c, t) where R(c, t) tends to zero exponentially fast as t tends to infinity. The precise behaviour of R(c, t) is established.

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