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PERTURBED MAP RISK MODELS WITH DIVIDEND BARRIER STRATEGIES

ERIC C. K. CHEUNG and DAVID LANDRIAULT
Journal of Applied Probability
Vol. 46, No. 2 (JUNE 2009), pp. 521-541
Stable URL: http://www.jstor.org/stable/25662441
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
PERTURBED MAP RISK MODELS WITH DIVIDEND BARRIER STRATEGIES
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Abstract

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.

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