The exponential estimate of the ultimate ruin probability for the non-homogeneous renewal risk model

Abstract

In this work, the non-homogeneous risk model is considered. In such a model, claims and inter-arrival times are independent but possibly non-identically distributed. The easily verifiable conditions are found such that the ultimate ruin probability of the model satisfies the exponential estimate exp{−ϱu} for all values of the initial surplus u  0. Algorithms to estimate the positive constant ϱ are also presented. In fact, these algorithms are the main contribution of this work. Sharpness of the derived inequalities is illustrated by several numerical examples.