Perturbed Risk Processes Analysed as Fluid Flows
by David Standford
Abstract: In this paper, 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 inter-claim 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 risk 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.
For More Information: Prof Daniel Dufresne at firstname.lastname@example.org Dr Aihua Xia at email@example.com