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The Resolvent and Expected Local Times for Markov-Modulated Brownian Motion with Phase-Dependent Termination Rates

Published online by Cambridge University Press:  30 January 2018

Lothar Breuer*
Affiliation:
University of Kent
*
Postal address: Institute of Mathematics and Statistics, University of Kent, Canterbury CT2 7NF, UK. Email address: l.breuer@kent.ac.uk
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Abstract

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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.

Type
Research Article
Copyright
© Applied Probability Trust 

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