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| STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS |
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Citation： |
CHEN Shuping,YONG Jiongmin.STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS[J].Chinese Annals of Mathematics B,2000,21(3):323~338 |
| Page view： 1573
Net amount： 848 |
Authors： |
CHEN Shuping; YONG Jiongmin |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.79790130), the National Distinguished Youth Science Foundation of China (No.19725106), and the Natural Science Foundation of the Ministry of Education of China (No.97024607). |
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| Abstract： |
This paper studies a 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. The authors introduce the stochastic Riccati equation for the LQ problem. This is a backward SDE with a complicated nonlinearity and a singularity. The local solvability of such a backward SDE is established, which by no means is obvious. For the case of deterministic coefficients, some further discussions on the Riccati equations have been carried out. Finally, an illustrative example is presented. |
Keywords： |
Stochastic LQ problem, Riccati equation, Backward stochastic differential equation, Malliavin calculus |
Classification： |
93E20, 49K45, 49N10, 60H10 |
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