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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.
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Abstract

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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

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