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Reflected Backward Stochastic Difference Equations with Finite State and their applications

Listed author(s):
  • Lifen An
  • Shaolin Ji
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    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.

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    Paper provided by in its series Papers with number 1001.3054.

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    Date of creation: Jan 2010
    Date of revision: 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, 05.
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