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This paper establishes the existence of a unique nonnegative continuousviscosity solution to the HJB equation associated with a Markovianlinear-quadratic control problems with singular terminal state constraint andpossibly unbounded cost coefficients. The existence result is based on a novelcomparison principle for semi-continuous viscosity sub- and supersolutions forPDEs with singular terminal value. Continuity of the viscosity solution isenough to carry out the verification argument.

Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint