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

2018/09/06 by Horst, Ulrich, Xia, Xiaonyu · 1 citation
#FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · doi:10.48550/arxiv.1809.01972

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. Continuity of the viscosity solution is enough to carry out the verification argument.

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