论文标题
反映了基于等级数据的向后随机微分方程
Reflected Backward Stochastic Differential Equation with Rank-based Data
论文作者
论文摘要
在本文中，我们研究了在马尔可夫框架中具有基于等级的数据的反映后退随机微分方程（反映了缩写中的BSDE）。也就是说，对反射BSDE的解决方案以最小的方式高于规定的边界过程，而反射的BSDE的发生器和终端值取决于基于等级的漂移和扩散系数的另一个随机微分方程（缩写中的SDE）的解决方案。我们将解决方案的规律性属性得出了这种反射的BSDE，并表明最初的启动时间$ t $和位置$ x $的解决方案是确定性函数，是针对某些障碍物问题（或变性不平等）的唯一粘度解决方案。
In this paper, we study reflected backward stochastic differential equation (reflected BSDE in abbreviation) with rank-based data in a Markovian framework; that is, the solution to the reflected BSDE is above a prescribed boundary process in a minimal fashion and the generator and terminal value of the reflected BSDE depend on the solution of another stochastic differential equation (SDE in abbreviation) with rank-based drift and diffusion coefficients. We derive regularity properties of the solution to such reflected BSDE, and show that the solution at the initial starting time $t$ and position $x$, which is a deterministic function, is the unique viscosity solution to some obstacle problem (or variational inequality) for the corresponding parabolic partial differential equation.
