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June 2013 The resolvent and expected local times for Markov-modulated Brownian motion with phase-dependent termination rates
Lothar Breuer
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J. Appl. Probab. 50(2): 430-438 (June 2013). DOI: 10.1239/jap/1371648951

Abstract

We consider a Markov-modulated Brownian motion (MMBM) with phase-dependent termination rates, i.e. while in a phase i the process terminates with a constant hazard rate ri ≥ 0. For such a process, we determine the matrix of expected local times (at zero) before termination and hence the resolvent. The results are applied to some recent questions arising in the framework of insurance risk. We further provide expressions for the resolvent and the local times at zero of an MMBM reflected at its infimum.

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Lothar Breuer. "The resolvent and expected local times for Markov-modulated Brownian motion with phase-dependent termination rates." J. Appl. Probab. 50 (2) 430 - 438, June 2013. https://doi.org/10.1239/jap/1371648951

Information

Published: June 2013
First available in Project Euclid: 19 June 2013

zbMATH: 1270.60078
MathSciNet: MR3102490
Digital Object Identifier: 10.1239/jap/1371648951

Subjects:
Primary: 60J25
Secondary: 60G51, 60J55

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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