Approximation formulae for compound poisson processes for a kind of claim distributions having a prescribed asymptotic behavior

摘要

The present contribution deals with an approximation for the compound Poisson process for large values of the operational time. Two cases are dealt with, according to the existence of the third or second moment of the individual claim distribution. The special feature of this claim distribution is its behavior for large values, i.e., fY(y) ≈ a0y + a1y2 + ⋯ + akyk + ⋯, (y → ∞). In these cases, an Edgeworth-like approximation is given.