A direct approach to linear-quadratic stochastic control

• Autorzy: Duncan T. E. , Pasik-Duncan B.

Identyfikatory

DOI

10.7494/OpMath.2017.37.6.821

• Języki publikacji: EN

Abstrakty

EN

A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.

Słowa kluczowe

EN

linear-quadratic Gaussian control; Riccati equation for optimization; stochastic control

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 6
• Strony: 821--827
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Duncan T. E.

• University of Kansas Department of Mathematics 503 Snow Hall, Lawrence, Kansas 66045, USA

autor

Pasik-Duncan B.

• University of Kansas Department of Mathematics 503 Snow Hall, Lawrence, Kansas 66045, USA

Bibliografia

• [1] V.I. Arnold, Characteristic class entering in quantization conditions, Funktsional'nyi Analiz i Ego Prilozheniya (Funct. Anal. Appl.) 1 (1967), 1-14.
• [2] V.I. Arnold, Mathematical Methods of Classical Mechanics, Grad. Texts in Math. 60, Springer, New York, 1978.
• [3] T.E. Duncan, Linear-quadratic stochastic differential games with general noise processes, Models and Methods in Economics and Management Science: Essays in Honor of Charles S. Tapiero (eds. F. El Ouardighi and K. Kogan), Operations Research and Management Series, Springer Intern. Publishing, Switzerland, vol. 198, 2014, 17-26.
• [4] T.E. Duncan, B. Pasik-Duncan, Linear quadratic fractional Gaussian control, SIAM J. Control. Optim. 51 (2013), 4604-4619.
• [5] T.E. Duncan, B. Maslowski, B. Pasik-Duncan, Linear-quadratic control for stochastic equations in a Hilbert space with fractional Brownian motions, SIAM J. Control Optim. 50 (2012), 507-531.
• [6] W.H. Fleming, R.W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, 1975.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).