Reflected Backward Stochastic Difference Equations with Finite State and their applications
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.
Keywords
Cite
@article{arxiv.1001.3054,
title = {Reflected Backward Stochastic Difference Equations with Finite State and their applications},
author = {Lifen An and Shaolin Ji},
journal= {arXiv preprint arXiv:1001.3054},
year = {2013}
}
Comments
We need to make a major change of this paper