Opuscula Math. 37, no. 6 (2017), 821-827
http://dx.doi.org/10.7494/OpMath.2017.37.6.821

 
Opuscula Mathematica

A direct approach to linear-quadratic stochastic control

Tyrone E. Duncan
Bozenna Pasik-Duncan

Abstract. 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.

Keywords: linear-quadratic Gaussian control, Riccati equation for optimization, stochastic control.

Mathematics Subject Classification: 93E20, 93C05.

Full text (pdf)

  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.
  • Tyrone E. Duncan
  • University of Kansas, Department of Mathematics, 503 Snow Hall, Lawrence, Kansas 66045, USA
  • Bozenna Pasik-Duncan
  • University of Kansas, Department of Mathematics, 503 Snow Hall, Lawrence, Kansas 66045, USA
  • Communicated by Marek Galewski.
  • Received: 2017-01-23.
  • Revised: 2017-04-03.
  • Accepted: 2017-04-08.
  • Published online: 2017-09-28.
Opuscula Mathematica - cover

Cite this article as:
Tyrone E. Duncan, Bozenna Pasik-Duncan, A direct approach to linear-quadratic stochastic control, Opuscula Math. 37, no. 6 (2017), 821-827, http://dx.doi.org/10.7494/OpMath.2017.37.6.821

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.