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  • Perturbed MAP Risk Models with Dividend Barrier Strategies

  • Part of
  • Eric C. K. Cheung, David Landriault
  • Journal:
    Journal of Applied Probability / Volume 46 / Issue 2 / June 2009
    Published online by Cambridge University Press:
    14 July 2016, pp. 521-541
    Print publication:
    June 2009
    • Article
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  • In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markov-modulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.