Journal of Applied Probability

Undiscounted Markov chain BSDEs to stopping times

Samuel N. Cohen

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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.

Article information

J. Appl. Probab., Volume 51, Number 1 (2014), 262-281.

First available in Project Euclid: 25 March 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 93E20: Optimal stochastic control 94C05: Analytic circuit theory

BSDE Markov chain uniform ergodicity risk averse control non-Ohmic circuit


Cohen, Samuel N. Undiscounted Markov chain BSDEs to stopping times. J. Appl. Probab. 51 (2014), no. 1, 262--281. doi:10.1239/jap/1395771428.

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