Abstract
Baoline Chen and Peter A. Zadrozny (2001) "Higher Moments in
Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control
Problem."
The paper obtains two principal results. First, using a new definition of higher-order
(>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 4th-order Taylor-series approximation of the objective
function of the linear-quadratic 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 2nd-order approximation of the finite-horizon LQEG objective function.
Using the simpler formulation, the present paper applies the perturbation method to derive
equations for computing a 4th-order approximation of the infinite-horizon 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.
Last Modified Date: July 19, 2008
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