Saddlepoint Approximations to Tail Probabilities a

Authors: Riccardo Gatto

Publish Date: 2011/03/03

Volume: 14, Issue: 4, Pages: 1053-1074

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Abstract

This article provides saddlepoint approximations to tail probabilities and quantiles of the insurer discounted total claim amount where the individual claim amounts are independent with a linear combination of exponential distributions and the number of claims is given by an inhomogeneous Poisson process with a periodic intensity function It extends some previous results by Gatto Methodol Comput Appl Probab 12533–551 2010 which are given for tail probabilities only and for nonperiodic intensities only Both extensions proposed in this article are important in the actuarial practice where phenomena generating claims are subject to seasonal variations and where the quantiles or the valuesatrisk of the total claim amount are desired Some numerical comparisons of the new methods with Monte Carlo simulation are shown The methods proposed are numerically very accurate computationally efficient and hence relevant for the actuarial practice

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