Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-26T02:17:38.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Stable Algorithms in Ruin Theory and Their Applications

Published online by Cambridge University Press:  29 August 2014

David C.M. Dickson ,
Alfredo D. Egídio dos Reis  and
Howard R. Waters
David C.M. Dickson*
Affiliation:
The University of Melbourne
Alfredo D. Egídio dos Reis*
Affiliation:
ISEG, Lisbon
Howard R. Waters*
Affiliation:
Heriot-Watt University, Edinburgh
*
Centre for Actuarial Studies, Faculty of Economics and Commerce, University of Melbourne, Parkville, Victoria 3052, Australia
Departamento de Matemática, Instituto Superior de Economia e Gestão Rua Miguel Lupi 20, P-1200 Lisbon, Portugal
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh Midlothian EH 14 4AS, Great Britain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we present a stable recursive algorithm for the calculation of the probability of ultimate ruin in the classical risk model. We also present stable recursive algorithms for the calculation of the joint and marginal distributions of the surplus prior to ruin and the severity of ruin. In addition we present bounds for these distributions.

Keywords

Probability of ruinSeverity of ruinSurplus prior to ruinRecursive calculationStable algorithmCompound binomial model
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 25 , Issue 2 , November 1995 , pp. 153 - 175
Copyright
Copyright © International Actuarial Association 1995

References

De Vylder, F. and Goovaerts, M.J. (1988) Recursive calculation of finite time ruin probabilities. Insurance: Mathematics and Economics, 7, 1–8.Google Scholar
Dickson, D.C.M. (1992) On the distribution of the surplus prior to ruin. Insurance: Mathematics and Economics, 11, 191–207.Google Scholar
Dickson, D.C.M. (1994) Some comments on the compound binomial model. ASTIN Bulletin, 24, 33–45.CrossRefGoogle Scholar
Dickson, D.C.M. and Dos Reis, A. E. (1994) Ruin problems and dual events. Insurance: Mathematics and Economics, 14, 51–60.Google Scholar
Dickson, D.C.M. and Waters, H. R. (1991) Recursive calculation of survival probabilities. ASTIN Bulletin, 21, 199–221.CrossRefGoogle Scholar
Dickson, D.C.M. and Waters, H. R. (1992) The probability and severity of ruin in finite and in infinite time. ASTIN Bulletin, 22, 177–190.CrossRefGoogle Scholar
Dos Reis, A. E. (1993) How long is the surplus below zero ? Insurance: Mathematics and Economics, 12, 23–38.Google Scholar
Dufresne, F. and Gerber, H.U. (1989) Three methods to calculate the probability of ruin. ASTIN Bulletin, 19, 71–90.CrossRefGoogle Scholar
Gerber, H.U. (1988) Mathematical fun with the compound binomial process. ASTIN Bulletin, 18, 161–168.CrossRefGoogle Scholar
Gerber, H.U., Goovaerts, M.J. and Kaas, R. (1987) On the probability and severity of ruin. ASTIN Bulletin, 17, 151–163.CrossRefGoogle Scholar
Goovaerts, M.J. and De Vylder, F. (1984) A stable recursive algorithm for evaluation of ultimate ruin probabilities. ASTIN Bulletin, 14, 53–59.CrossRefGoogle Scholar
Panjer, H.H. (1981) Recursive calculation of a family of compound distributions. ASTIN Bulletin, 12, 22–26.CrossRefGoogle Scholar
Panjer, H.H. (1986) Direct calculation of ruin probabilities. Journal of Risk and Insurance, 53, 521–529.CrossRefGoogle Scholar
Panjer, H.H. and Lutek, B. (1983) Practical aspects of stop-loss calculations. Insurance: Mathematics and Economics, 2, 159–177.Google Scholar
Panjer, H.H. and Wang, S. (1993) On the stability of recursive formulas. ASTIN Bulletin, 23, 227–258.CrossRefGoogle Scholar
Panjer, H.H. and Willmot, G. E. (1992) Insurance Risk Models. Society of Actuaries, Schaumberg, IL.Google Scholar
Shiu, E.S.W. (1989) The probability of eventual ruin in the compound binomial model. ASTIN Bulletin, 19, 179–190.CrossRefGoogle Scholar
Willmot, G.E. (1992) Ruin probabilities in the compound binomial model. Insurance: Mathematics and Economics, 12, 133–142.Google Scholar