Simple approximations of ruin probabilities (Q2740067)

This paper deals with the classical model of an insurance risk business where the claims occur according to a Poisson process \(N(t)\) with intensity \(\alpha\) and the costs of the claims are described by a sequence \(z_{k},\;k=1,2,\ldots\), of i.i.d. random variables with distribution function \(F\). The risk process is defined by \(X(t)=ct-\sum_{k=1}^{N(t)}z_{k}\), where \(c>0\) is a constant corresponding to the premium income. For the ruin probability \(\Psi(u)\) of the company facing the risk process \(X\) and having the initial capital \(u\), the author considers ``simple'' approximations which use only some moments of \(F\), such as diffusion approximation, De Vylder approximation, Rényi approximation, and makes comparisons of these simple approximations.