- Economics - Research Publications
Economics - Research Publications
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ItemA general class of risk modelsDUFRESNE, DANIEL ( 2002-01)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.
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ItemOn the expected discounted penalty function at ruin of a surplus process with interestCai, Jun ; Dickson, David C.M. ( 2001-11)In this paper, we study the expected value of a discounted penalty function at ruin of the classical surplus process modified by the inclusion of interest of the surplus. The 'penalty' is simply a function of the surplus immediately prior to ruin and the deficit at ruin. An integral equation for the expected value is derived, while the exact solution is given when the initial surplus is zero. Dickson's (1992) formulae for the distribution of the surplus immediately prior to ruin in the classical surplus process are generalised to our modified surplus process.