This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems 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. Under a mild additional assumption on the model parameters we show that the viscosity solution is in fact a \pi-strong solution to the HJB equation and can hence be compactly approximated by smooth functions .
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems 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 .
R
Under a mild additional assumption on the model parameters we show that the
Continuity of the
R
in fact a \pi-strong solution to the HJB equation and can hence be compactly approximated by smooth functions
enough to carry out the verification argument