Stochastic maximum principle in the Pontryagin's form for wide band noise driven systems

Abstract

The control problems for wide band noise driven systems have the following specific feature. A wide band noise is given by its autocovariance function. At the same time, different wide band noises may have the same autocovariance function. Therefore, it is important to obtain the results which are invariant under the change of wide band noises, corresponding to the same autocovariance function. In this paper, one such result is obtained: a stochastic maximum principle in the Pontryagin's form is proved for a control system driven by a state-dependent wide band noise. The result is demonstrated on an example of controlled stochastic differential equation of risky asset price.