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Exit problems for reflected Markov-modulated Brownian motion

Breuer, Lothar (2012) Exit problems for reflected Markov-modulated Brownian motion. Journal of Applied Probability, 49 (3). pp. 697-709. ISSN 0021-9002. (doi:10.1239/jap/1346955327) (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:31237)

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/10.1239/jap/1346955327

Abstract

Let (?, ?) denote a Markov-modulated Brownian motion (MMBM) and denote its supremum process by S. For some a > 0, let ? (a) denote the time when the reflected process ? := S -- ? first surpasses the level a. Furthermore, let ?_(a) denote the last time before ? (a) when ? attains its current supremum. In this paper we shall derive the joint distribution of S?(a), ?_(a), and ?(a), where the latter two will be given in terms of their Laplace transforms. We also provide some remarks on scale matrices for MMBMs with strictly positive variation parameters. This extends recent results for spectrally negative Lévy processes to MMBMs. Due to well-known fluid embedding and state-dependent killing techniques, the analysis applies to Markov additive processes with phase-type jumps as well. The result is of interest to applications such as the dividend problem in insurance mathematics and the buffer overflow problem in queueing theory. Examples will be given for the former.

Item Type: Article
DOI/Identification number: 10.1239/jap/1346955327
Uncontrolled keywords: exit problem, Markov additive process, Markov-modulated Brownian motion, reflection
Subjects: Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
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 07:19 UTC
Last Modified: 16 Nov 2021 10:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31237 (The current URI for this page, for reference purposes)

University of Kent Author Information

Breuer, Lothar.

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