A generalised Gerber-Shiu measure for Markov-additive risk processes with phase-type claims and capital injections

Breuer, Lothar and Badescu, Andrei (2013) A generalised Gerber-Shiu measure for Markov-additive risk processes with phase-type claims and capital injections. Scandinavian Actuarial Journal . ISSN 0346-1238. (In press) (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1080/03461238.2011.636969

Abstract

In this paper we consider a risk reserve process where the arrivals (either claims or capital injections) occur according to a Markovian point process. Both claim and capital injection sizes are phase-type distributed and the model allows for possible correlations between these and the inter-claim times. The premium income is modelled by a Markov-modulated Brownian motion which may depend on the underlying phases of the point arrival process. For this risk reserve model we derive a generalised Gerber–Shiu measure that is the joint distribution of the time to ruin, the surplus immediately before ruin, the deficit at ruin, the minimal risk reserve before ruin, and the time until this minimum is attained. Numeral examples illustrate the influence of the parameters on selected marginal distributions.

Item Type: Article
Uncontrolled keywords: Gerber-Shiu function, Markov-additive process, phase-type, capital injections, time value of ruin
Subjects: Q Science > Operations Research - Theory
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Lothar Breuer
Date Deposited: 04 Oct 2012 07:30
Last Modified: 23 Jan 2013 09:50
Resource URI: http://kar.kent.ac.uk/id/eprint/31240 (The current URI for this page, for reference purposes)
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