Opuscula Math. 37, no. 6 (2017), 821-827

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.

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  • 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.
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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

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