In classical risk theory, the surplus process is a very important model for understanding how the capital or surplus of an insurance company evolves over time. By adding to the previous surplus the current premium flow and deducting the claims made during the period, the process gives the value of the capital that is available to the insurer at each point in time. Each period is tracked so that the surplus never gets below zero because if it does, it provides an indication of ruin, that is, the company is in ap osition of negative cashflow. However, the first time that ruin occurs is important and the company must ensure this does not happen because it can leave the company inoperable. This time to ruin is so much a function of the initial capital and the pricing structure of the insurer’s book of business, although how claims evolve over time can also directly impact the level of surplus. Claims generally are out of the company’s control, but it can manage its surplus so that it can predictably estimate the level of claims that will emerge over time. One distinguishing feature of a typical mathematical structure of the surplus process is the assumption that individual claims do arise independently. We know that this assumption of independence is no longer realistic and reasonable because individual risks, although homogeneous, typically share common characteristics that claims from one can induce claims of another. In other words, the risks do not exhibit independence. In this paper, we investigate the probability structure of the time to ruin when the individual claims are not independent. However, unlike the case of independence where there may be a more tractable solution, it is not straightforward to get closed form solutions to the probability of ruin. Instead, we apply simulation procedures to provide us insight into the statistical distribution of the time to ruin when claims are dependent. We find that in the presence of dependent claims, the time to ruin occurs so much faster.

Abstract In classical risk theory, the surplus process is a very important model for understand-