Global $C^{1}$ regularity of the value function in optimal stopping problems
Global $C^{1}$ regularity of the value function in optimal stopping problems
复制标题
最优停止问题中价值函数的全局 $C^{1}$ 正则性
DOI：
10.1214/19-aap1517
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
G. Peskir
中科院分区：
文献类型：
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作者：
T. Angelis;G. Peskir
证明了如果过程是强Feller且边界点对于停集是概率正则的，或者过程是强Markov且边界点对于停集内部是概率正则的，则边界点对于停集是绿色正则的.结合这一含义的过程中的连续可微流的存在，我们表明，价值函数是连续可微的最佳停止边界时，增益函数是这样的。推导出的事实，在抛物和椭圆的情况下的唯一假设的概率正则性的最佳停止边界的边值问题，从而改善已知的分析结果在偏微分方程文献中，并建立事实的第一次在积分微分方程的情况下。证明的方法是纯粹的概率和概念简单。应用的例子包括第一个已知的概率证明的事实，即时间导数的价值函数在美国把问题是连续的最佳停止边界。
We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the stopping set, then the boundary point is Green regular for the stopping set. Combining this implication with the existence of a continuously differentiable flow of the process we show that the value function is continuously differentiable at the optimal stopping boundary whenever the gain function is so. The derived fact holds both in the parabolic and elliptic case of the boundary value problem under the sole hypothesis of probabilistic regularity of the optimal stopping boundary, thus improving upon known analytic results in the PDE literature, and establishing the fact for the first time in the case of integro-differential equations. The method of proof is purely probabilistic and conceptually simple. Examples of application include the first known probabilistic proof of the fact that the time derivative of the value function in the American put problem is continuous across the optimal stopping boundary.
从最佳停止边界到 Rost 的反向障碍和 Skorokhod 嵌入
DOI：
10.48550/arxiv.1505.02724
发表时间：
2015
期刊：
--
影响因子：
--
作者：
De Angelis T
通讯作者：
De Angelis T