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On Markovian solutions to Markov Chain BSDEs

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

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