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arXiv · 1809.01972

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

Ulrich Horst·Xiaonyu Xia
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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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Ulrich Horst, Xiaonyu Xia. 2020-04-28. Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint. https://arxiv.org/abs/1809.01972

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