Perturbed Risk Processes Analyzed as Fluid Flows

Ren, J. and Breuer, Lothar and Stanford, D. and Yu, K. (2009) Perturbed Risk Processes Analyzed as Fluid Flows. Stochastic Models, 25 (3). pp. 522-544. ISSN 1532-6349. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1080/15326340903088867

Abstract

In this article, we present a unified phase-type approach for calculating ruin probabilities for a class of perturbed risk processes, which includes the perturbed Sparre-Andersen process with phase-type interclaim time and claim size distributions, the perturbed Markov-modulated risk process, and the MAP/PH risk process as well. The key to the solution method is the identification for a given risk process of a parallel Markov-modulated fluid flow. The resulting group of perturbed risk processes amenable to this approach we refer to as the Markov-modulated fluid-flow equivalent (MFE) class, as the ability to find an equivalent fluid flow is the only limiting factor in our analysis. The primary contributions of this work are 1) the unified, tractable, phase-type structures for the maximal aggregate loss and ladder height distributions for all variants of perturbed risk processes belonging to the MFE class, and 2) the explicit formulas for the ruin probability for all variants in this class. The full breadth of the models is illustrated through a diverse range of examples.

Item Type: Article
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Lothar Breuer
Date Deposited: 04 Jan 2010 11:41
Last Modified: 20 Apr 2012 13:45
Resource URI: http://kar.kent.ac.uk/id/eprint/23450 (The current URI for this page, for reference purposes)
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