Controlled Diffusions under Full, Partial and Decentralized Information: Existence of Optimal Policies and Discrete-Time Approximations

TL;DR

This paper establishes existence and discrete-time approximation results for optimal control policies in continuous-time stochastic control problems across fully observed, partially observed, and decentralized information structures, enabling practical computation of near-optimal solutions.

Contribution

It provides the first comprehensive existence and approximation results for partially observed and decentralized models, extending the applicability of discrete-time methods.

Findings

Existence of optimal policies under various information structures.

Discrete-time approximation schemes for continuous-time control problems.

Applicability of discrete-time methods to decentralized stochastic control.

Abstract

We present existence and discrete-time approximation results on optimal control policies for continuous-time stochastic control problems under a variety of information structures. These include fully observed models, partially observed models and multi-agent models with decentralized information structures. While there exist comprehensive existence and approximations results for the fully observed setup in the literature, few prior research exists on discrete-time approximation results for partially observed models. For decentralized models, even existence results have not received much attention except for specialized models and approximation has been an open problem. Our existence and approximations results lead to the applicability of well-established partially observed Markov decision processes and the relatively more mature theory of discrete-time decentralized stochastic control to be applicable for computing near optimal solutions for continuous-time stochastic control.