Open AccessA multidimensional singular stochastic control problem on a finite time horizon
Author(s) -
Marcin Boryc,
Łukasz Kruk
Publication year - 2015
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2015.69.1.23
Subject(s) - hamilton–jacobi–bellman equation , bounded function , mathematics , stochastic control , bellman equation , optimal control , derivative (finance) , time horizon , function (biology) , horizon , mathematical analysis , mathematical optimization , evolutionary biology , financial economics , economics , biology , geometry
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.