Stochastic filtering under model ambiguity

Abstract

In this paper, we study a non-linear filtering problem when the signal model is uncertain. The model ambiguity is characterized by a class of probability measures from which the true probability measure is taken. The optimal filter can be estimated by converting to a conditional mean field optimal control problem. In the first part of this article, we develop a general form stochastic maximum principle for a conditional mean-field type model driven by a forward and backward control system. In the second part, we characterize the ambiguity filter and prove its existence and uniqueness.