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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: dcmd@unimelb.edu.au
S. Drekic
Affiliation:
Department of Statistics & Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada., Email: sdrekic@math.uwaterloo.ca
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Abstract

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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

Information

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

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