Collective Risk Theory

Abstract

Abstract In this article, classical continuous‐time surplus process and its variations are introduced; several assumptions for the number of claims and for the times between claims are proposed. The time of ruin, the probability of ruin, and the surplus immediately before and at ruin caused by a claim are defined. Then an upper bound on and an asymptotic formula for the probability of ruin are given. Also, the mean discounted penalty is proposed, which is usually used to study a variety of interesting and important quantities, for example, moments and distribution functions. Finally, the maximal aggregate loss and the associated compound geometric distribution are discussed.

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