发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究状态约束随机控制中的目标生成Dirichlet问题，通过粘性不等式和比较原理证明边界方程解的存在唯一性，并应用于集值边界控制、无界漂移及冗余对冲等场景。
AI 中文摘要
我们研究具有标量盈余$R \geq 0$的状态约束随机控制问题。当$R$的漂移和波动率在零处消失时，控制定义了一个低维的Hamilton-Jacobi-Bellman方程。从逐控制的状态约束粘性不等式出发，我们证明了内部值的上极限和下极限分别是该边界方程的下解和上解。终端相容性和比较原理确定了它们的共同极限。我们要求正盈余漂移和生成元增长的单侧界，以及边界生成元的支配条件。对于紧致或强制控制，这些条件可由局部下界和边界控制集的连续性得出。对于光滑的随机目标值$w$，变换$R = Y - w(t,X)$使可行上图像变平，并且在所述假设下，边界控制值提供了Dirichlet数据。应用包括集值边界控制、具有二次成本的无界漂移，以及具有非恒定目标边界的冗余对冲工具。
英文摘要
We study state-constrained stochastic control problems with a scalar surplus $R \geq 0$. Controls for which the drift and volatility of $R$ vanish at zero define a lower-dimensional Hamilton-Jacobi-Bellman equation. Starting from control-wise state-constraint viscosity inequalities, we prove that the upper and lower limits of the interior value are a subsolution and a supersolution of this boundary equation. Terminal compatibility and comparison identify their common limit. We require one-sided bounds on positive surplus drift and generator growth, together with domination by boundary generators. For compact or coercive controls, these follow from a local lower bound and continuity of the boundary control set. For a smooth stochastic target value $w$, the transformation $R = Y - w(t,X)$ flattens the viable epigraph, and, under the stated hypotheses, the boundary control value supplies the Dirichlet datum. Applications include set-valued boundary controls, unbounded drift with quadratic costs, and redundant hedging instruments with a nonconstant target boundary.
Comments25 pages
