Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-14T03:49:37.131Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier

Published online by Cambridge University Press:  17 April 2015

Hans U. Gerber ,
X. Sheldon Lin  and
Hailiang Yang
Hans U. Gerber
Affiliation:
at the University of Hong Kong, École des hautes études commerciales, Université de Lausanne, CH-1015 Lausanne, Switzerland, E-mail: hgerber@unil.ch.
X. Sheldon Lin
Affiliation:
Department of Statistics, University of Toronto, Toronto, Ontario M5S 3G3 Canada, E-mail: sheldon@utstat.utoronto.ca.
Hailiang Yang
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, E-mail: hlyang@hkusua.hku.hk.
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.

For a general class of risk models, the dividends-penalty identity is derived by probabilistic reasoning. This identity is the key for understanding and determining the optimal dividend barrier, which maximizes the difference between the expected present value of all dividends until ruin and the expected discounted value of a penalty at ruin (which is typically a function of the deficit at ruin). As an illustration, the optimal barrier is calculated in two classical models, for different penalty functions and a variety of parameter values.

Keywords

General class of risk modelsdividends-penalty identitypenalty at ruinoptimal dividend barrierBrownian motioncompound Poisson process
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 2 , November 2006 , pp. 489 - 503
Copyright
Copyright © ASTIN Bulletin 2006

References

Albrecher, H., Claramunt, M.M. and Mármol, M. (2005) “On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times”, Insurance: Mathematics and Economics, 37, 324–334.Google Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory, Springer-Verlag, Berlin.Google Scholar
Chan, B., Gerber, H.U. and Shiu, E.S.W. (2006) “Discussion of Xiaowen Zhou’s ‘On a classical risk model with a constant dividend barrier’”, North American Actuarial Journal, 10(2), 133–139.CrossRefGoogle Scholar
De Finetti, B. (1957) “Su un’ impostazione alternativa della teoria collettiva del rischio,” Transactions of the XVth International Congress of Actuaries, 2, 433–443.Google Scholar
Frostig, E. (2005) “The expected time to ruin in a risk process with constant barrier via martingales”, Insurance: Mathematics and Economics, 37, 216–228.Google Scholar
Dickson, D.C.M. and Waters, H.R. (2004) “Some optimal dividends problems”, ASTIN Bulletin, 34, 49–74.CrossRefGoogle Scholar
Gerber, H.U. (1972) “Games of economic survival with discrete- and continuous-income process”, Operations Research, 20(1), 37–45.CrossRefGoogle Scholar
Gerber, H.U. and Shiu, E.S.W. (1998) “On the time value of ruin”, North American Actuarial Journal, 2(1), 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
Gerber, H.U. and Shiu, E.S.W. (2005) “The time value of ruin in a Sparre Andersen model,” North American Actuarial Journal 9(2), 49–84.CrossRefGoogle Scholar
Gerber, H.U. and Shiu, E.S.W. (2006) “On optimal dividend strategies in the compound Poisson model”, North American Actuarial Journal 10(2), 76–93.CrossRefGoogle Scholar
Gerber, H.U., Shiu, E.S.W. and Smith, N. (2006) “Maximizing dividends without bankruptcy”, ASTIN Bulletin 36, 5–23.CrossRefGoogle Scholar
Li, S. and Garrido, J. (2004) “On a class of renewal models with a constant dividend barrier”, Insurance: Mathematics and Economics, 35, 697–701.Google Scholar
Lin, X.S. and Pavlova, K. (2006) “The compound Poisson risk model with a threshold dividend strategy”, Insurance: Mathematics and Economics, 38, 57–80.Google Scholar
Lin, X.S., Willmot, G.E. and Drekic, S. (2003) “The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function”, Insurance: Mathematics and Economics, 33, 551–566.Google Scholar
Yuen, K.C., Wang, G. and Li, W.K. (2006) “The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier”, Insurance: Mathematics and Economics To appear.CrossRefGoogle Scholar