| Issue |
ESAIM: COCV
Volume 19, Number 1, January-March 2013
|
|
|---|---|---|
| Page(s) | 78 - 90 | |
| DOI | https://doi.org/10.1051/cocv/2011206 | |
| Published online | 23 February 2012 | |
Equivalent cost functionals and stochastic linear quadratic optimal control problems∗
School of Economics, Shandong University,
Jinan
250100, P.R.
China
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
26
October
2010
Revised:
16
November
2011
Abstract
This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear optimization problems.
Mathematics Subject Classification: 93E20 / 49N10 / 60H10
Key words: Stochastic LQ problem / stochastic Hamiltonian system / Forward-backward stochastic differential equation / Riccati equation / stochastic maximum principle
This work is supported by the National Natural Science Foundation of China (11026185, 11101242), the Natural Science Foundation of Shandong Province, China (ZR2010AQ004), and the Independent Innovation Foundation of Shandong University (2009TS036).
© EDP Sciences, SMAI, 2012
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