A practical solution to the problem of ultimate ruin probability

Abstract

Abstract In a heuristic way, comparable to the method used by Bohman (1977) in the derivation of his rule of thumb, we find an approximation to the probability of ruin in an infinite time period, in the classical risk model. The solution is practical because our formula is very simple and because it uses only the three first moments of the distribution function of one claim. The risk reserve Yt at the instant t depends, among other things, on the expected number λ. of claims in one year, the expected cost α of one claim, the security loading η. We replace the stochastic process Yt (t⩾0) by a stochastic process Y′ t (t⩾0), also interpreted as a risk reserve, in such a way that (i) the distribution function of one claim cost is 1 − e−x/α′ in the new process, (ii) the new parameters λ′, α′, η′ are fixed in such a way that fd_114_1 Then the probability of ultimate ruin in the initial process is approximated by the probability of ruin in the new process. We verified the quality of the approximation on almost a...