Optimal Dividends in the Dual Model with Diffusion
UNSW Australian School of Business Research Paper No. 2008ACTL10
24 Pages Posted: 26 Aug 2008
Date Written: July 25, 2008
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
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