关键词: Probability of ruin, the perturbed classical surplus model, Oscillation, recursive calculation

Abstract:

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.

Key words: Probability of ruin, the perturbed classical surplus model, Oscillation, recursive calculation