Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest.
type: Item
instance of: scholarly article
title: Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest.
zbMATH Open document ID: 1074.91028
DOI: 10.1016/S0167-6687(02)00204-4
author: Jun Cai
author: David C. M. Dickson
published in: Insurance Mathematics \& Economics
publication date: 2003-11-16T00:00:00Z
review text: According to the Sparre Andersen model, the surplus at time \(t\) is given by \[ U(t)=u+ct-Z(t),\;t\geq 0 \] where \(c>0\) is the rate of premium income, \(Z(t)\) is the aggregate claim amount up to time \(t\) and \(U(0)=u\). In the paper this model is modified, assuming that the insurer receives interest on the surplus at a constant continuously compound force of interest \(\delta\). So, denoted by \(\tau_{\delta}\) the time of ruin for the modified surplus process, the ultimate ruin probability is given by \[ \psi_{\delta}(u) =Pr\{\tau_{\delta}<\infty\}. \] The authors provide exponential type upper bounds for \(\psi_{\delta}(u)\) by means of martingale and recursive techniques. Moreover numerical comparisons of the upper bounds obtained by each techniques are presented.
reviewed by: Emilia Di Lorenzo
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 91B70
zbMATH DE Number: 2004070
zbMATH Keywords: Sparre Andersen model
zbMATH Keywords: compound Poisson model
zbMATH Keywords: ruin probability
zbMATH Keywords: adjustment coefficient
MaRDI profile type: Publication
cites work: Ruin probabilities with compounding assets
cites work: Q3868650
cites work: Aspects of risk theory
cites work: Q5754578
cites work: Q5781688
cites work: Ruin estimates under interest force
cites work: The adjustment function in ruin estimates under interest force
cites work: RPA pathwise derivative estimation of ruin probabilities
cites work: Lundberg approximations for compound distributions with insurance applications
full work available at URL: s0167-6687(02)00204-4
OpenAlex ID: W2027056093
description: scientific article; zbMATH DE number 2004070