The ruin probability of the renewal model with constant interest force and upper-tailed independent heavy-tailed claims
type: Item
instance of: scholarly article
title: The ruin probability of the renewal model with constant interest force and upper-tailed independent heavy-tailed claims
zbMATH Open document ID: 1201.91096
author: Xinmei Shen
author: Zhengyan Lin
publication date: 2010-11-17T00:00:00Z
review text: The paper provides a simple formula for the probability of ruin under a special case of the Sparre Andersen risk model where, in addition, interest is earned at a constant force of interest. More precisely, claims are assumed to arrive at random times, which are independent and identically distributed. The sizes of the claims are identically distributed nonnegative random variables that are independent from the interclaim times. It is also assumed that claim sizes follow some heavy-tailed distribution and the dependence between any two claim sizes follows some pre-specified structure. The article's main focus is on the tail distribution of the aggregate claims and on asymptotic properties of the finite-time ruin probability. The explicit expressions that are derived are simple and applicable in any situation where the claim-size distribution is known. As a whole, the paper is clearly written and provides detailed proofs. It relies somewhat on the previous literature on the subject for motivating the research and discussing its outcome. Despite these slight shortcomings, the paper is a pleasant and smooth reading.
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 5816596
zbMATH Keywords: asymptotic estimate
zbMATH Keywords: consistent variation
zbMATH Keywords: renewal process
zbMATH Keywords: upper-tail independent
zbMATH Keywords: finite-time ruin probability
reviewed by: Kristina P. Sendova
MaRDI profile type: Publication
full work available at URL: s10114-010-7574-0
OpenAlex ID: W2053743357
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DOI: 10.1007/S10114-010-7574-0
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5816596