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A direct approach to linear-quadratic stochastic control

Duncan T. E., Pasik-Duncan B.

Opuscula Mathematica

2017

Vol. 37, no. 6

821--827

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.