Series Solution of Discrete Time Stochastic Optimal Control Problems

TL;DR

This paper introduces a method to compute solutions to discrete time stochastic optimal control problems using Taylor polynomial approximations of the Dynamic Programming Equations, applicable over finite and infinite horizons.

Contribution

It presents a novel approach to solve stochastic control problems by degree-by-degree computation of Taylor polynomial solutions to Dynamic Programming Equations.

Findings

Taylor polynomials can be computed degree by degree for these problems

Applicable to both finite and infinite time horizons

Provides a systematic method for solving complex stochastic control problems

Abstract

In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic Programming Equations can be computed degree by degree.