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Stochastic Linear Quadratic Optimal Control Problems

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Abstract.

This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward—backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China , People's Republic of China

    S. Chen

  2. Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics,and Institute of Mathematical Finance, Fudan University, Shanghai 200433, People's Republic of China , People's Republic of China

    J. Yong

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  1. S. Chen
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  2. J. Yong
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Accepted 15 May 2000. Online publication 1 December 2000

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Chen, S., Yong, J. Stochastic Linear Quadratic Optimal Control Problems. Appl Math Optim 43, 21–45 (2001). https://doi.org/10.1007/s002450010016

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  • DOI: https://doi.org/10.1007/s002450010016

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