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Optimal Dividends in the Dual Model with Diffusion

Published online by Cambridge University Press:  17 April 2015

Benjamin Avanzi  and
Hans U. Gerber
Benjamin Avanzi
Affiliation:
Actuarial Studies, Australian School of Business, UNSW Sydney NSW 2052, Australia, E-mail: b.avanzi@unsw.edu.au
Hans U. Gerber
Affiliation:
at The University of Hong Kong, University of Lausanne, Faculty of Business and Economics, 1015 Lausanne, Switzerland, E-mail: hgerber@unil.ch
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Abstract

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In the dual model, the surplus of a company is a Lévy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be calculated, if a barrier strategy is applied, and how the optimal dividend barrier can be determined. Conditions for optimality are discussed and several numerical illustrations are given. Furthermore, a family of models is analysed where the individual gain amount distribution is rescaled and compensated by a change of the Poisson parameter.

Keywords

Optimal dividendsBarrier strategiesDual modelSmooth pasting conditionJump-diffusionLaplace transforms
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 2 , November 2008 , pp. 653 - 667
Copyright
Copyright © ASTIN Bulletin 2008

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