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

Breuer, Lothar, Badescu, Andrei (2014) A generalised Gerber-Shiu measure for Markov-additive risk processes with phase-type claims and capital injections. Scandinavian Actuarial Journal, 2014 (2). pp. 93-115. ISSN 0346-1238. E-ISSN 1651-2030. (doi:10.1080/03461238.2011.636969) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31240)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
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
DOI/Identification number: 10.1080/03461238.2011.636969
Uncontrolled keywords: Gerber-Shiu function, Markov-additive process, phase-type, capital injections, time value of ruin
Subjects: Q Science > Operations Research - Theory
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Lothar Breuer
Date Deposited: 04 Oct 2012 07:30 UTC
Last Modified: 17 Aug 2022 10:56 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31240 (The current URI for this page, for reference purposes)

University of Kent Author Information

Breuer, Lothar.

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