Optimal Dividends in the Dual Model with Diffusion

UNSW Australian School of Business Research Paper No. 2008ACTL10

24 Pages Posted: 26 Aug 2008

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Hans Ulrich Gerber

University of Lausanne

Date Written: July 25, 2008

Abstract

In the dual model, the surplus of a company is a Levy 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 dividends, Barrier strategies, Dual model, Smooth pasting condition, Jump-diffusion, Laplace transforms

JEL Classification: C00, G20, G23, G24, G31, G32, G35

Suggested Citation

Avanzi, Benjamin and Gerber, Hans Ulrich, Optimal Dividends in the Dual Model with Diffusion (July 25, 2008). UNSW Australian School of Business Research Paper No. 2008ACTL10. Available at SSRN: https://ssrn.com/abstract=1258094 or http://dx.doi.org/10.2139/ssrn.1258094

Benjamin Avanzi (Contact Author)

UNSW Australia Business School, School of Risk and Actuarial Studies ( email )

UNSW Sydney, NSW 2052
Australia

Hans Ulrich Gerber

University of Lausanne ( email )

Quartier Chambronne
Lausanne, Vaud CH-1015
Switzerland

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