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

Ulrich Horst and Xiaonyu Xia

Papers from arXiv.org

Abstract: 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.

Date: 2018-09
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