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.
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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.
