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On Markovian solutions to Markov Chain BSDEs

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  • Samuel N. Cohen
  • Lukasz Szpruch

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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  • Samuel N. Cohen & Lukasz Szpruch, 2011. "On Markovian solutions to Markov Chain BSDEs," Papers 1111.5739, arXiv.org.
  • Handle: RePEc:arx:papers:1111.5739
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    File URL: http://arxiv.org/pdf/1111.5739
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    References listed on IDEAS

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    1. Peter Carr & Helyette Geman & Dilip Madan & Marc Yor, 2004. "From local volatility to local Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 581-588.
    2. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    3. repec:dau:papers:123456789/1448 is not listed on IDEAS
    4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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