A Note on the Continuity of Free-Boundaries in Finite-Horizon Optimal Stopping Problems for One-Dimensional Diffusions
A Note on the Continuity of Free-Boundaries in Finite-Horizon Optimal Stopping Problems for One-Dimensional Diffusions
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一维扩散有限视野最优停止问题中自由边界连续性的一个注解
DOI：
10.1137/130920472
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
T. Angelis
中科院分区：
文献类型：
--
作者：
T. Angelis
我们给出了一类一般的有限时间最优停止问题自由边界连续的充分条件，例如在金融和经济领域。其基本过程是一维时齐随机微分方程(SDE)的强解。该证明依赖于解析和概率论证，并基于偏微分方程组理论中的最大值原理启发的矛盾方案。要求SDE系数具有温和的局部正则性，并要求增益函数在边界处局部光滑性。
We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising, for instance, in finance and economics. The underlying process is a strong solution of a one-dimensional, time-homogeneous stochastic differential equation (SDE). The proof relies on both analytic and probabilistic arguments and is based on a contradiction scheme inspired by the maximum principle in partial differential equations theory. Mild, local regularity of the coefficients of the SDE and smoothness of the gain function locally at the boundary are required.