A semiparametric technique to estimate survival probabilities

The role of the so-called surplus processes in the assessment of probability of survival of a company is well-known in risk theory and applications thereof. However, the insurance models used in this regard ignore the fact that, in many situations, no relevant information is available for the assessment of survival after the company goes out of business. In this paper, we revisit the classical risk model in order to remedy this situation. Having stopped the deficit process, which is negative of the surplus process, at the time of ruin, under two different sampling schemes, we obtain inference procedure for ruin probabilities. As by products of our methodology, we also obtain procedures to assess the reliability of systems whose survival depends on a cumulative damage process, which is equivalent to the aggregate claim size process of the classical risk model.