Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint
Mathematical Finance
2020-04-29 v3
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.
Cite
@article{arxiv.1809.01972,
title = {Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint},
author = {Ulrich Horst and Xiaonyu Xia},
journal= {arXiv preprint arXiv:1809.01972},
year = {2020}
}