Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T20:53:05.208Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Dividends Under a Ruin Probability Constraint

Published online by Cambridge University Press:  10 May 2011

D. C. M. Dickson  and
S. Drekic
D. C. M. Dickson
Affiliation:
Centre for Actuarial Studies, Department of Economics, University of Melbourne, Victoria 3010, Australia., Email: [email protected]
S. Drekic
Affiliation:
Department of Statistics & Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada., Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a classical surplus process modified by the payment of dividends when the insurer's surplus exceeds a threshold. We use a probabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present value of dividend payments subject to a constraint on the insurer's ruin probability.

Keywords

DividendsRuin ProbabilityTime of RuinSeverity of Ruin
Type
Papers
Information
Annals of Actuarial Science , Volume 1 , Issue 2 , September 2006 , pp. 291 - 306
Copyright
Copyright © Institute and Faculty of Actuaries 2006

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

De Vylder, F. (1978). A practical solution to the problem of ultimate ruin probability. Scandinavian Actuarial Journal, 114–119.CrossRefGoogle Scholar
Dickson, D.C.M. (1991). The probability of ultimate ruin with a variable premium loading — a special case. Scandinavian Actuarial Journal, 75–86.CrossRefGoogle Scholar
Dickson, D.C.M. (2005). Insurance risk and ruin. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (2004). Some optimal dividends problems. ASTIN Bulletin, 34, 49–74.CrossRefGoogle 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. (1998). On the time value of ruin. North American Actuarial Journal, 2(1), 48–72.CrossRefGoogle Scholar
Gerber, H.U. & Shiu, E.S.W. (2004). Optimal dividends: analysis with Brownian motion. North American Actuarial Journal, 8(1), 1–20.CrossRefGoogle Scholar
Gerber, H.U. & Shiu, E.S.W. (2006). On optimal dividend strategies in the compound Poisson model. North American Actuarial Journal, 10(2), 76–93.CrossRefGoogle Scholar
Højgaard, B. (2002). Optimal dynamic premium control in non-life insurance. Maximising dividend pay-outs. Scandinavian Actuarial Journal, 225–245.CrossRefGoogle Scholar
Lin, X.S. & Pavlova, K. (2006). The compound Poisson risk model with a threshold dividend strategy. Insurance: Mathematics & Economics, 38, 57–80.Google Scholar
Paulsen, J. (2003). Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics, 7, 457–473.CrossRefGoogle Scholar