Time-symmetric optimal stochastic control problems in space-time domains
Probability
2020-07-07 v1 Optimization and Control
Abstract
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves two adjoint optimal stopping times adapted to a pair of filtrations, the traditional increasing one and another, decreasing. They are the keys of the time symmetry of the construction, which can be regarded as a generalization of "Schr\"odinger's problem" (1931-32) to space-time domains. The relation with the notion of "Hidden diffusions" is also described.
Cite
@article{arxiv.2007.02110,
title = {Time-symmetric optimal stochastic control problems in space-time domains},
author = {Ana Bela Cruzeiro and Carlos Oliveira and Jean-Claude Zambrini},
journal= {arXiv preprint arXiv:2007.02110},
year = {2020}
}