Perturbed MAP risk models with dividend barrier strategies
Eric C. K. Cheung and David Landriault
Source: J. Appl. Probab. Volume 46, Number 2 (2009), 521-541.
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.
Primary Subjects: 60J75
Secondary Subjects: 60J25, 60J60
Keywords: Markovian arrival; perturbed process; barrier strategy; Gerber--Shiu function; discounted dividend payment
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676104
Digital Object Identifier: doi:10.1239/jap/1245676104
Zentralblatt MATH identifier:
05578823
Mathematical Reviews number (MathSciNet):
MR2535830
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