On Markovian solutions to Markov Chain BSDEs

Samuel N. Cohen; Lukasz Szpruch

doi:10.3934/naco.2012.2.257

Article Contents

2012, Volume 2, Issue 2: 257-269. Doi: 10.3934/naco.2012.2.257

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On Markovian solutions to Markov Chain BSDEs

Samuel N. Cohen^1, and
Lukasz Szpruch^1,

1.
Mathematical Institute, University of Oxford, 24-29 St Giles, OX1 3LB, Oxford

Received: November 2011

Revised: March 2012

Published: April 2012

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Abstract

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs.

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Mathematics Subject Classification: Primary: 60J27; Secondary: 60H05, 34A12.

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