Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications
Mathematics Department, UNICAMP-State University of Campinas, Rua Sérgio Buarque de Holanda, 651, 13083-859, Campinas, Brazil
Accepted: 26 May 2021
Published online: 6 June 2021
In this survey we present the near-optimal stochastic control problem according to some recent tools in the literature. In particular, we focus on the approach of a discretization of the noise values instead of the canonical time-discretization. This is the so called skeleton structure. This allows to obtain an -optimal control in non-Markovian systems (the main Theorem). A simple example illustrates the technique. The importance of the approach is emphasised in a final section on open problems related to more geometrical framework and discontinuous noise.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021