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 { − ϱ u } 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.

Keywords

• non-homogeneous model
• renewal risk model
• ruin probability
• net profit condition
• Lundberg’s inequality