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1 results

  • Optimal Dividends in the Dual Model with Diffusion

  • Benjamin Avanzi, Hans U. Gerber
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 38 / Issue 2 / November 2008
    Published online by Cambridge University Press:
    17 April 2015, pp. 653-667
    Print publication:
    November 2008
    • Article
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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.