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

Fotis Loukissas,Alex Karagrigoriou

doi:10.33889/ijmems.2022.7.1.010

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.

Highlights

IntroductionThe occurrence of extreme value events has become increasingly frequent
As indicated in the Introduction our aim in this work is the study of the uniform asymptotic behavior of ruin probability within S which represents the class of subexponential distributions
In this work we focus and investigate the uniform asymptotic behavior of ruin probability within the class of strongly subexponential distributions which constitute a special subclass of subexponential distributions known to provide a convenient framework for studying large classes of heavy tailed distributions

Summary

Introduction

The occurrence of extreme value events has become increasingly frequent. Extreme events could happen in complex computer systems and in construction projects. The consequences of these events are, in many occasions, catastrophic when financial and social aspects are involved. Risk theory and ruin probabilities are considered to be important parts of insurance mathematics. In practice Value-at-Risk and Expected Shortfall are typical risk measures, ruin theory retains a key role for risk handling and management in actuarial science and in various other applied probability areas such as queueing theory or mathematical finance (see e.g. Kostyuchenko, 2018). There is a need to develop prediction theories and actuarial methods for analyzing the ruin probabilities of such events. In order to develop these theoretical tools, random variables (like the claims in insurance companies) with heavy tailed distributions are applied

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Results

Conclusion