A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.
@article{bwmeta1.element.ojs-doi-10_17951_a_2015_69_1_23,
author = {Marcin Boryc and \L ukasz Kruk},
title = {A multidimensional singular stochastic control problem on a finite time horizon},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {69},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_1_23}
}
Marcin Boryc; Łukasz Kruk. A multidimensional singular stochastic control problem on a finite time horizon. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 69 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_1_23/
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