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Undiscounted Markov Chain BSDEs to Stopping Times

Part of: Markov processes Stochastic systems and control Circuits, networks

Published online by Cambridge University Press:  30 January 2018

Samuel N. Cohen
Samuel N. Cohen*
Affiliation:
University of Oxford
*
∗ Postal address: Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK. Email address: samuel.cohen@maths.ox.ac.uk
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Abstract

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We consider backward stochastic differential equations in a setting where noise is generated by a countable state, continuous time Markov chain, and the terminal value is prescribed at a stopping time. We show that, given sufficient integrability of the stopping time and a growth bound on the terminal value and BSDE driver, these equations admit unique solutions satisfying the same growth bound (up to multiplication by a constant). This holds without assuming that the driver is monotone in y, that is, our results do not require that the terminal value be discounted at some uniform rate. We show that the conditions are satisfied for hitting times of states of the chain, and hence present some novel applications of the theory of these BSDEs.

Keywords

BSDEMarkov chainuniform ergodicityrisk averse controlnon-Ohmic circuit

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 93E20: Optimal stochastic control 94C05: Analytic circuit theory
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 262 - 281
Copyright
© Applied Probability Trust 

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