On the informational structure in optimal dynamic stochastic control

TL;DR

This paper develops a general framework for optimal dynamic stochastic control with control-dependent information, analyzing informational consistency and Bellman's principle within natural filtrations of stochastic processes.

Contribution

It introduces a broad framework accommodating control-dependent informational structures and proves Bellman's principle in this context.

Findings

Established a general formulation for control-dependent information structures.

Proved Bellman's principle under the new framework.

Analyzed informational consistency in natural filtrations.

Abstract

We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman's principle is formulated and proved. In a series of related results, we expound on the informational structure in the context of (completed) natural filtrations of stochastic processes.