This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a linear-quadratic stochastic control problem with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for semi-continuous viscosity sub- and supersolutions for PDEs with singular terminal value. Continuity of the viscosity solution is enough to carry out the verification argument.

中文翻译：

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具有奇异终端状态约束的线性二次随机控制问题的连续粘度解

本文建立了HJB方程唯一的非负连续黏性解的存在性，该解与具有奇异终端状态约束和可能无穷大的成本系数的线性二次随机控制问题相关。存在的结果是基于一种新颖的比较原理，用于具有奇异终值的PDE的半连续粘度子解和上解。粘度溶液的连续性足以执行验证论证。