论文标题
在对数增长和应用下具有两个障碍的一维反射BSDE
One dimensional reflected BSDEs with two barriers under logarithmic growth and applications
论文作者
论文摘要
在本文中，我们解决了一个维度反射的向后反射的随机微分方程的存在和解决方案的唯一性，当发电机允许对数增长$（| y | y | y | y | y || y ||+| z | z | | \ sqrt {| sqrt {| \ ln | z | z $ y y $ y y y y y y n oble Growth $（| y | y || y | y | y | y | y | y | y | y | y | y || y | y | y | y | y | y | y | y | y | y | y | y | y ||终端值$ξ$和障碍过程$（l_t）_ {0 \ leq t \ leq t} $和$（u_t）_ {0 \ leq t \ leq t} $是$ l^p $ - 构建适用于合适的$ p> 2 $。主要思想是利用本地解决方案的概念来构建全局。作为应用程序，我们扩大了混合零和随机差异游戏的功能类别的类别，并且相关的双重障碍偏微分方程问题具有独特的粘度解决方案。
In this paper we deal with the problem of the existence and the uniqueness of a solution for one dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator is allowing a logarithmic growth $(|y||\ln|y||+|z|\sqrt{|\ln|z||})$ in the state variables $y$ and $z$. The terminal value $ξ$ and the obstacle processes $(L_t)_{0\leq t\leq T}$ and $(U_t)_{0\leq t\leq T}$ are $L^p$-integrable for a suitable $p > 2$. The main idea is to use the concept of local solution to construct the global one. As applications, we broaden the class of functions for which mixed zero-sum stochastic differential games admit an optimal strategy and the related double obstacle partial differential equation problem has a unique viscosity solution.
