Volume 24, Number 4, October–December 2018
|Page(s)||1849 - 1879|
|Published online||13 March 2019|
Linear quadratic control problems of stochastic Volterra integral equations*
School of Mathematics, Sichuan University,
** Corresponding author: firstname.lastname@example.org
Accepted: 5 January 2017
This paper is concerned with linear quadratic control problems of stochastic differential equations (SDEs, in short) and stochastic Volterra integral equations (SVIEs, in short). Notice that for stochastic systems, the control weight in the cost functional is allowed to be indefinite. This feature is demonstrated here only by open-loop optimal controls but not limited to closed-loop optimal controls in the literature. As to linear quadratic problem of SDEs, some examples are given to point out the issues left by existing papers, and new characterizations of optimal controls are obtained in different manners. For the study of SVIEs with deterministic coefficients, a class of stochastic Fredholm−Volterra integral equations is introduced to replace conventional forward-backward SVIEs. Eventually, instead of using convex variation, we use spike variation to obtain some additional optimality conditions of linear quadratic problems for SVIEs.
Mathematics Subject Classification: 93E20 / 49N10 / 45D05
Key words: Stochastic Volterra integral equations / stochastic Fredholm−Volterra integral equations / stochastic linear quadratic problems / spike variation
© EDP Sciences, SMAI 2019
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