The moments of ruin time in the classical risk model with discrete claim size distribution
type: Item
instance of: scholarly article
title: The moments of ruin time in the classical risk model with discrete claim size distribution
zbMATH Open document ID: 0957.62089
DOI: 10.1016/S0167-6687(98)00025-0
author: Philippe Picard
author: Claude Lefèvre
published in: Insurance Mathematics \& Economics
publication date: 2001-03-20T00:00:00Z
review text: The authors consider a classical ruin model with discrete claim sizes \(W_i\), constant claim intensity \(c\) and constant premium rate \(\lambda\). Exact simple solutions are provided for the moments \(k\) of ruin time for the case where the initial reserve \(u=0\). Also, for the case of \(u\) natural, an analytic expression is derived. The calculation involves recursive calculations in terms of \(k\) and \(u\) which can be rolled out into finite sums over \(r,\dots,u\). The calculations are built on a generalized Appell structure of polynomials. Both cases \(c>\) and \(c\leq\lambda E[W_i]\) are treated.
reviewed by: Thomas Siegl
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 1251567
zbMATH Keywords: ruin theory
zbMATH Keywords: risk theory
MaRDI profile type: Publication
cites work: A remark on the moments of ruin time in classical risk theory
cites work: Martingales in Markov processes applied to risk theory
cites work: The numerical solution of the Schmitter problems: Theory
cites work: Numerical Finite-Time Ruin Probabilities by the Picard-Lef vre Formula
cites work: Q3868650
cites work: When does the surplus reach a given target?
cites work: On the first crossing of the surplus process with a given upper barrier
cites work: The probability of ruin in finite time with discrete claim size distribution
cites work: On the Ruin Problem of Collective Risk Theory
cites work: Q5592832
cites work: Q3228000
full work available at URL: s0167-6687(98)00025-0
OpenAlex ID: W1974560982
description: scientific article; zbMATH DE number 1251567