摘要翻译：
本文首先建立了有限状态反射倒向随机差分方程（简称FS-RBSDEs）。然后用“一步法”研究了存在唯一性定理和比较定理。研究了FS-RBSDEs与最优停车时间问题之间的联系，并证明了Knightian不确定下的多先验最优停车问题是FS-RBSDEs的特例。作为副产品，我们发展了有限状态下离散时间G-鞅的一般理论，包括Doob-Mayer分解定理和可选抽样定理。最后，我们考虑了完全市场和不完全市场中美式期权的定价模型。
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英文标题：
《Reflected Backward Stochastic Difference Equations with Finite State and
  their applications》
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作者：
Lifen An, Shaolin Ji
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最新提交年份：
2013
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  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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PDF链接：
https://arxiv.org/pdf/1001.3054