On the Moments of the Time of Ruin with Applications to Phase-Type Claims

Steve Drekic and Gordon Willmot

North American Actuarial Journal, 2005, vol. 9, issue 2, 17-30

Abstract: We describe an approach to the evaluation of the moments of the time of ruin in the classical Poisson risk model. The methodology employed involves the expression of these moments in terms of linear combinations of convolutions involving compound negative binomial distributions. We then adapt the results for use in the practically important case involving phase-type claim size distributions. We present numerical examples to illuminate the influence of claim size variability on the moments of the time of ruin.

Date: 2005
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DOI: 10.1080/10920277.2005.10596195

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