Two-sided bounds of ruin probabilities

Abstract

A new method for obtaining two-sided bounds of ruin probabilities is proposed. This is based on the analysis of so-called geometric sums which are sums of i.i.d.r.v.'s and the number of summands is a r.v. also having a geometric distribution. The method uses probabilistic arguents only and does not use analytic relations such as Spitzer identity. It is shown that some well known bounds can be proved with the help of the developed method. Numerical examples are considered.

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