Approximation of the Initial Reserve for Known Ruin Probabilities

摘要

An important problem in the study of actual risk theory is approximating the probability of ruin within finite time based on a specified initial reserve. This paper addresses the similar, but mathematically different, problem of how to approximate a desired initial reserve given a pre-specified probability of ruin. Although the procedures have desirable asymptotic properties such as consistency and asymptotic normality, these are computer-intensive and would not have been practicable before the wide spread availability of high-speed computers. The procedures rely on simulated realizations of a general risk process. Thus, these can be used in many of the mathematical models of risk processes that appear in the literature such as the Compound Poisson, ARMA and Stochastic Discounting models. Examples of several models are given to demonstrate the versatility of the procedure and to demonstrate that the procedures are computationally feasible. (Author)