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Reflected Backward Stochastic Difference Equations with Finite State and their applications

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  • Lifen An
  • Shaolin Ji

Abstract

In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method. The connections between FS-RBSDEs and optimal stopping time problems are investigated and we also show that the optimal stopping problems with multiple priors under Knightian uncertainty is a special case of our FS-RBSDEs. As a byproduct we develop the general theory of g-martingales in discrete time with finite state including Doob-Mayer Decomposition Theorem and Optional Sampling Theorem. Finally, we consider the pricing models of American Option in both complete and incomplete markets.

Suggested Citation

  • Lifen An & Shaolin Ji, 2010. "Reflected Backward Stochastic Difference Equations with Finite State and their applications," Papers 1001.3054, arXiv.org, revised Dec 2012.
    • Handle: RePEc:arx:papers:1001.3054
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    1. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
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    Cited by:

    1. Monia Karouf, 2019. "Reflected and Doubly Reflected Backward Stochastic Differential Equations with Time-Delayed Generators," Journal of Theoretical Probability, Springer, vol. 32(1), pages 216-248, March.

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