Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-25T07:18:47.562Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Optimal Dividends Problems

Published online by Cambridge University Press:  17 April 2015

David C.M. Dickson  and
Howard R. Waters
David C.M. Dickson
Affiliation:
Centre for Actuarial Studies, Department of Economics, University of Melbourne, Victoria 3010, Australia, Email: dcmd@unimelb.edu.au
Howard R. Waters
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, Great Britain, Email: H.R.Waters@ma.hw.ac.uk
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.

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 1 , May 2004 , pp. 49 - 74
Copyright
Copyright © ASTIN Bulletin 2004

References

Asmussen, S. and Taksar, M. (1997) Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics & Economics 20, 1–15.Google Scholar
Borch, K. (1990) Economics of Insurance. North Holland, Amsterdam.Google Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer-Verlag, Berlin.Google Scholar
Claramunt, M.M., Mármol, M. and Alegre, A. (2002) Expected present value of dividends with a constant barrier in the discrete time model. Proceedings of the 6th International Congress on Insurance: Mathematics & Economics, Lisbon.Google Scholar
De Finetti, B. (1957) Su un’ impostazione alternativa dell teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries 2, 433–443.Google Scholar
De Vylder, F. and Goovaerts, M.J. (1988) Recursive calculation of finite time survival probabilities. Insurance: Mathematics & Economics 7, 1–8.Google Scholar
Dickson, D.C.M. and Gray, J.R. (1984) Approximations to ruin probability in the presence of an upper absorbing barrier. Scandinavian Actuarial Journal, 105–115.CrossRefGoogle Scholar
Dickson, D.C.M. and Waters, H.R. (1991) Recursive calculation of survival probabilities. ASTIN Bulletin 21, 199–221.CrossRefGoogle Scholar
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation, Philadelphia, PA.Google Scholar
Gerber, H.U. and Shiu, E.S.W. (1998) On the time value of ruin. North American Actuarial Journal 2, 48–78.CrossRefGoogle Scholar
Gerber, H.U. and Shiu, E.S.W. (2004) Optimal dividends: analysis with Brownian motion. North American Actuarial Journal 8(1), 1–20.CrossRefGoogle Scholar
Højgaard, B. (2002) Optimal dynamic premium control in non-life insurance. Maximising dividend pay-outs. Scandinavian Actuarial Journal, 225–245.CrossRefGoogle Scholar
Klugman, S.A., Panjer, H.H. and Willmot, G.E. (1998) Loss models – from data to decisions. John Wiley, New York.Google Scholar
Lin, X.S., Willmot, G.E. and Drekic, S. (2003) The classical Poisson risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function. Insurance: Mathematics & Economics 33, 551–566.Google Scholar
Pafumi, G. (1998) Discussion of ‘On the time value of ruin’. North American Actuarial Journal 2, 75–76.CrossRefGoogle Scholar
Paulsen, J. and Gjessing, H.K. (1997) Optimal choice of dividend barriers for a risk process with stochastic return on investments. Insurance: Mathematics & Economics 20, 215–223.Google Scholar
Siegl, T. and Tichy, R.E. (1999) A process with stochastic claim frequency and a linear dividend barrier. Insurance: Mathematics & Economics 24, 51–65.Google Scholar