On Markovian solutions to Markov Chain BSDEs

2011/11/24 by Cohen, Samuel N., Szpruch, Lukasz
#34A12 #60H05 #60J27 #Classical Analysis and ODEs (math.CA) #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1111.5739

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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