Uniform Asymptotic Probability for Multi Renewal Risk Model with Strong Subexponential Tailed Claims

Abstract

In this paper, we study the uniform asymptotic behavior for the ruin probability in a continuous time renewal counting process. For the proposed model, we assume that the financial claims for each extreme event are compensated by a finite number of independent insurance companies. Moreover, it is assumed that the claims of each insurance company is a sequence of random variables the tail distribution of which belongs to the class of subexponential distributions with finite mean. More specifically the objective of this work is the study of the uniform asymptotic behavior of ruin probability within the class of strongly subexponential distributions, a subclass of subexponential distributions, which provides a convenient framework for investigating heavy tailed distributions. The results are established for two types of asymptotic relations, namely for the common ruin probability of insurance companies and also for the ruin probability of at least one insurance company.

Keywords

• insurance risk
• heavy tailed distributions
• subexponential tails
• ruin probability
• renewal model
• k-th dimensional risk model
• uniform asymptotic theory