Equivalent cost functionals and stochastic linear quadratic optimal control problems∗
School of Economics, Shandong University,
Revised: 16 November 2011
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
© EDP Sciences, SMAI, 2012