Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiums
type: Item
instance of: scholarly article
title: Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiums
zbMATH Open document ID: 1231.91178
author: Yinghua Dong
author: Yuebao Wang
published in: Journal of Industrial and Management Optimization
publication date: 2012-01-18T00:00:00Z
review text: The paper focuses on renewal risk models, overcoming the restrictive hypothesis about the mutual independence of the claim sizes, on the basis of specific references to some applicative cases. The starting point consists of the well-known risk-model involving the surplus U: \[ U(t)=e^{R_t}\left (x+c\int_0^t e^{R_u}du-\sum_{k=1}^{N(t)}X_ke^{R_{\tau_k}}\right ),\qquad t\geq 0 \] where \(U(0)\) represents the initial capital, \(c\) the premium rate, \(N(t)\) the claim number, \(X_k\) the \(k\)-th claim size, the \(X_k\) variables being nonnegative, identically distributed but not necessarily independent; moreover the price process is depicted by a geometric Lévy process \(\{e^{R_t}, t\geq 0\}\), the \(X_k\), \(N(t)\) and \(R_t\) variables are mutually independent. The inter-claim times are nonnegative i.i.d. random variables. Within the above nonstandard model, where the claim sizes and premium sizes are identically distributed and upper-tail independent random variables, respectively, the dependence structures involving claim sizes and inter-claim times are studied; in the case of claim size distribution belonging to the extended-regular-varying class, asymptotic results for stochastically discounted aggregate claims are provided. Uniform estimates for the finite and infinite-time ruin probability are proved under specific assumptions about the the tail of the premium-size distribution.
reviewed by: Emilia Di Lorenzo
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 5998541
zbMATH Keywords: ruin probability
zbMATH Keywords: Lévy process
zbMATH Keywords: renewal risk models
MaRDI profile type: Publication
full work available at URL: jimo.2011.7.849
OpenAlex ID: W2321973498
DOI: 10.3934/JIMO.2011.7.849
description: scientific article; zbMATH DE number 5998541