On the expected discounted penalty function at ruin of a surplus process with interest.
type: Item
instance of: scholarly article
title: On the expected discounted penalty function at ruin of a surplus process with interest.
zbMATH Open document ID: 1074.91027
DOI: 10.1016/S0167-6687(02)00120-8
author: Jun Cai
author: David C. M. Dickson
published in: Insurance Mathematics \& Economics
publication date: 2003-11-16T00:00:00Z
review text: The paper deals with the ruin problem for an insurer, who receives interest on its surplus at time \(t\), \(U_{\delta}(t)\), at the constant force \(\delta\) per unit time. In particular the expected value of a discounted penalty function at ruin is investigated. Denoted by \(T_{\delta}\) the time of ruin, \(u\) the inizial surplus and \(\alpha\) a non-negative parameter, the expected value of a discounted function of the surplus immediately prior to ruin and the deficit at ruin is given by \[ \Phi_{\delta,\alpha}(u)=E(w(U(T_{\delta}^-),| U(T_{\delta})| )e^{-\alpha T_{\delta}} I(T_{\delta}<\infty)), \] where \(I(A)\) is the indicator function of a set \(A\) and \(w\) is a non-negative function. The authors provide an integral equation involving \(\Phi_{\delta,\alpha}\) and obtain the exact solution for \(\Phi_{\delta,0}(0)\). Finally some classical formulae concerning the distribution of the surplus immediately prior to ruin are generalized to the surplus process with interest.
reviewed by: Emilia Di Lorenzo
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 91B70
zbMATH DE Number: 2004025
zbMATH Keywords: ruin penalty function
zbMATH Keywords: surplus prior to ruin
zbMATH Keywords: deficit at ruin
zbMATH Keywords: Laplace transform
zbMATH Keywords: Volterra equation
MaRDI profile type: Publication
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full work available at URL: s0167-6687(02)00120-8
OpenAlex ID: W1976822036
description: scientific article; zbMATH DE number 2004025