Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem
Baoline Chen and
Computational Economics, 2003, vol. 21, issue 1_2, 45-64
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.
References: Add references at CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed
Downloads: (external link)
Access to the full text of the articles in this series is restricted.
Journal Article: Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem (2003)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:kap:compec:v:21:y:2003:i:1_2:p:45-64
Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2
Access Statistics for this article
Computational Economics is currently edited by Hans Amman
More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla ().