Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-31T12:04:20.770Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Finite Time Ruin Problems

Published online by Cambridge University Press:  10 May 2011

D. C. M. Dickson
D. C. M. Dickson
Affiliation:
Centre for Actuarial Studies, Department of Economics, University of Melbourne, Victoria 3010, Australia., Email: dcmd@unimelb.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

In the classical risk model, we use probabilistic arguments to write down expressions in terms of the density function of aggregate claims for joint density functions involving the time to ruin, the deficit at ruin and the surplus prior to ruin. We give some applications of these formulae in the cases when the individual claim amount distribution is exponential and Erlang(2).

Keywords

Finite Time RuinJoint DensityDeficit at Ruin

Information

Type
Papers
Information
Annals of Actuarial Science , Volume 2 , Issue 2 , September 2007 , pp. 217 - 232
Copyright
Copyright © Institute and Faculty of Actuaries 2007

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.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. & Stegun, I.A. (1965). Handbook of mathematical functions. Dover, New York.Google Scholar
Cheung, E.C.K., Dickson, D.C.M. & Drekic, S. (2007). Moments of discounted dividends for a threshhold strategy in the compound Poisson risk model. Unpublished manuscript.Google Scholar
Dickson, D.C.M. (2008). Some explicit solutions for the joint density of the time of ruin and the deficit at ruin. ASTIN Bulletin, 38, 259–276.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (1992). The probability and severity of ruin in finite and in infinite time. ASTIN Bulletin, 22, 177–190.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (2006). Optimal dynamic reinsurance. ASTIN Bulletin, 36, 415–432.CrossRefGoogle Scholar
Dickson, D.C.M. & Willmot, G.E. (2005). The density of the time to ruin in the classical Poisson risk model. ASTIN Bulletin, 35, 45–60.CrossRefGoogle Scholar
Dickson, D.C.M., Hughes, B.D. & Lianzeng, Z. (2005). The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims. Scandinavian Actuarial Journal, 5, 358–376.CrossRefGoogle Scholar
Drekic, S. & Willmot, G.E. (2003). On the density and moments of the time to ruin with exponential claims. ASTIN Bulletin, 33, 11–21.CrossRefGoogle Scholar
Erdélyi, A. (ed.) (1954). Tables of integral transforms, Volume 1. McGraw-Hill, New York.Google Scholar
Gerber, H.U. (1979). An introduction to mathematical risk theory. S.S. Huebner Foundation, Philadelphia, PA.Google Scholar
Gerber, H.U. & Shiu, E.S.W. (1997). The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance: Mathematics & Economics, 21, 129–137.Google Scholar
Gradshteyn, L.S. & Ryzhik, L.M. (1994). Table of integrals, series, and products (Fifth edition). Academic Press, San Diego.Google Scholar
Liu, G. & Zhao, J. (2007). Joint distributions of some actuarial random vectors in the compound binomial model. Insurance: Mathematics & Economics, 40, 95–103.Google Scholar
Prabhu, N.U. (1961). On the ruin problem of collective risk theory. Annals of Mathematical Statistics, 32, 757–764.CrossRefGoogle Scholar
Seal, H.L. (1978). Survival probabilities. John Wiley & Sons, New York.Google Scholar
Willmot, G.E. & Woo, J.K. (2007). On the class of Erlang mixtures with risk theoretic applications. North American Actuarial Journal, 11(2), 99–115.CrossRefGoogle Scholar
Wu, R., Wang, G. & Wei, L. (2003). Joint distributions of some actuarial random vectors containing the time of ruin. Insurance: Mathematics & Economics, 33, 147–161.Google Scholar