A multidimensional singular stochastic control problem on a finite time horizon | Zendy

Marcin Boryc | Zendy; Łukasz Kruk | Zendy

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A 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-sklodowska 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.

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