Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-09-19T04:55:15.125Z Has data issue: false hasContentIssue false
  • English
  • Français

A finite-time ruin probability formula for continuous claim severities

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Zvetan G. Ignatov  and
Vladimir K. Kaishev
Zvetan G. Ignatov*
Affiliation:
Sofia University ‘St Kliment Ohridski’
Vladimir K. Kaishev*
Affiliation:
City University, London
*
∗ Postal address: Faculty of Economics and Business Administration, Sofia University ‘St Kliment Ohridski’, 125 Tsarigradsko Shosse Boulevard, bl. 3, Sofia 1113, Bulgaria.
∗∗ Postal address: Faculty of Actuarial Science and Statistics, Cass Business School, City University, 106 Bunhill Row, London EC1 8TZ, UK. Email address: v.kaishev@city.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

Keywords

Risk processPoisson claim arrivalpremium-income functionclaim severities distributionfinite-time ruin probabilityAppell polynomial

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 570 - 578
Copyright
Copyright © Applied Probability Trust 2004 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Dimitrova, D. S., Ignatov, Z. G., and Kaishev, V. K. (2003). Finite time ruin probabilities for continuous claim severities. Actuarial Res. Paper 150, Faculty of Actuarial Science and Statistics, Cass Business School, City University, London.Google Scholar
Ignatov, Z. G., and Kaishev, V. K. (2000). Two sided bounds for the finite time probability of ruin. Scand. Actuarial J. 2000, 46–62.Google Scholar
Ignatov, Z. G., Kaishev, V. K., and Krachunov, R. S. (2001). An improved finite-time ruin probability formula and its Mathematica implementation. Insurance Math. Econom. 29, 375–386.Google Scholar
Johnson, N., and Kotz, S. (1994). Distributions in Statistics: Continuous Multivariate Distributions. John Wiley, New York.Google Scholar
Karlin, S., and Taylor, H. M. (1981). A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
Kaz´min, Yu. A. (1988). Appell polynomials. In Encyclopedia of Mathematics, Vol. 1, ed. Hazewinkel, M., Kluwer, Dordrecht, pp. 209–210.Google Scholar
Picard, P. and Lefèvre, C. (1997). The probability of ruin in finite time with discrete claim size distribution. Scand. Actuarial J. 1997, 58–69.Google Scholar