BLS Working Papers: Higher Moments in Perturbation Solution of the LinearQuadratic Exponential Gaussian Optimal Control Problem 

Author:
 Chen, Baoline 
ISBN:  9781491257838 
Publication Date:  Aug 2013 
Publisher:  CreateSpace Independent Publishing Platform

Book Format:  Paperback 
List Price:  USD $15.99 
Book Description:

The paper obtains two principal results. First, using a new definition of higherorder (>2) matrix derivatives, the paper derives a recursion for computing any Gaussian multivariate moment. Second, the paper uses this result in a perturbation method to derive equations for computing the 4thorder Taylor series approximation of the objective function of the linearquadratic exponential Gaussian (LQEG) optimal control problem. Previously, Karp (1985) formulated the 4th multivariate...
More DescriptionThe paper obtains two principal results. First, using a new definition of higherorder (>2) matrix derivatives, the paper derives a recursion for computing any Gaussian multivariate moment. Second, the paper uses this result in a perturbation method to derive equations for computing the 4thorder Taylor series approximation of the objective function of the linearquadratic exponential Gaussian (LQEG) optimal control problem. Previously, Karp (1985) formulated the 4th multivariate Gaussian moment in terms of MacRae's definition of a matrix derivative. His approach extends with difficulty to any higher (>4) multivariate Gaussian moment. The present recursion straightforwardly computes any multivariate Gaussian moment. Karp used his formulation of the Gaussian 4th moment to compute a 2ndorder approximation of the finitehorizon LQEG objective function. Using the simpler formulation, the present paper applies the perturbation method to derive equations for computing a 4thorder approximation of the infinitehorizon LQEG objective function. By illustrating a convenient definition of matrix derivatives in the numerical solution of the LQEG problem with the perturbation method, the paper contributes to the computational economist's toolbox for solving stochastic nonlinear dynamic optimization problems.