Recursive calculation of the probability and severity of ruin

D. C M Dickson

Research output: Contribution to journalArticle

Abstract

In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. © 1989.

Original languageEnglish
Pages (from-to)145-148
Number of pages4
JournalInsurance: Mathematics and Economics
Volume8
Issue number2
Publication statusPublished - Jun 1989

Fingerprint

Risk Theory
Ruin Probability
Recursive Method
Gamma distribution
G-function
Exponential distribution
Explicit Solution
Calculate
Alternatives
Model

Keywords

  • Probability of ruin
  • Severity of ruin

Cite this

@article{3674fb0ed4fa40d6a9f2664d977b277b,
title = "Recursive calculation of the probability and severity of ruin",
abstract = "In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. {\circledC} 1989.",
keywords = "Probability of ruin, Severity of ruin",
author = "Dickson, {D. C M}",
year = "1989",
month = "6",
language = "English",
volume = "8",
pages = "145--148",
journal = "Insurance: Mathematics and Economics",
issn = "0167-6687",
publisher = "Elsevier",
number = "2",

}

Recursive calculation of the probability and severity of ruin. / Dickson, D. C M.

In: Insurance: Mathematics and Economics, Vol. 8, No. 2, 06.1989, p. 145-148.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Recursive calculation of the probability and severity of ruin

AU - Dickson, D. C M

PY - 1989/6

Y1 - 1989/6

N2 - In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. © 1989.

AB - In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. © 1989.

KW - Probability of ruin

KW - Severity of ruin

UR - http://www.scopus.com/inward/record.url?scp=0011473033&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 145

EP - 148

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

IS - 2

ER -