Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T03:10:00.481Z Has data issue: false hasContentIssue false
  • English
  • Français

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
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.

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

References

Avanzi, B. (2008) A review of modern collective risk theory with dividend strategies. UNSW Australian School of Business Research Paper No. 2008ACTL09. Google Scholar
Avanzi, B., Gerber, H.U. and Shiu, E.S.W. (2007) Optimal dividends in the dual model. Insurance: Mathematics and Economics 41(1), 111–123.Google Scholar
Azcue, P. and Muler, N. (2005) Optimal reinsurance and dividend distribution policies in the Cramér-Lundberg model. Mathematical Finance 15(2), 261–308.CrossRefGoogle Scholar
Bayraktar, E. and Egami, M. (2008) Optimizing venture capital investments in a jump diffusion model. Mathematical Methods of Operations Research 67(1), 21–42.CrossRefGoogle Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer-Verlag, Berlin Heidelberg New York.Google 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
Gerber, H.U. (1972) Games of economic survival with discrete- and continuous-income processes. Operations Research 20(1), 37–45.CrossRefGoogle Scholar
Gerber, H.U. and Landry, B. (1998) On the discounted penalty at ruin in a jump-diffusion and the perpetual put option. Insurance: Mathematics and Economics 22(3), 263–276.Google 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
Miyasawa, K. (1962) An economic survival game. Journal of the Operations Research Society of Japan 4(3), 95–113.Google Scholar
Pafumi, G. (1998) Discussion on H.U. Gerber and E.S.W. Shiu’s “On the time value of ruin”. North American Actuarial Journal 2(1), 5–76.Google Scholar
Schmidli, H. (2008) Stochastic Control in Insurance. Probability and its Applications. Springer-Verlag, London. Google Scholar