A general class of risk models
University of Melbourne Author/sDufresne, Daniel
AffiliationEconomics and Commerce: Centre for Actuarial Studies
CitationsDufresne, Daniel (2002) A general class of risk models.
Access StatusOpen Access
ISBN 0734021879 research paper no. 94
We consider the actuarial risk model when the waiting times or claims have a Laplace transform which is a rational function. This generalizes the classical model, where the waiting times are expotenial, and give more flexibility in the modelling of a risk business. Ruin is seen as a random walk crossing a barrier; the summands of the random walk are expressed as the difference of the waiting time and the claim. The class R of distributions which have finite Laplace transforms includes the so-called phase-type distributions. For waiting times in R , the Laplace transform of the ruin probability is obtained explicitly; if the calims are in R , then the probability of ruin is a combination of exponentials times polynomials, which can be found in closed-form.
KeywordsRisk theory; Laplace transform; renewal process; random walk.
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