Volume 26, 2020
|Number of page(s)||29|
|Published online||14 February 2020|
Necessary conditions of Pontraygin’s type for general controlled stochastic Volterra integral equations*
School of Mathematics, Sichuan University,
610065, PR China.
** Corresponding author: firstname.lastname@example.org
Accepted: 23 December 2019
This article is addressed to giving a solution to a unsolved problem, i.e., to establish the necessary optimality conditions of Pontraygin’s type for controlled stochastic Volterra integral equations (SVIEs) when the control region is non-convex and the control variable enters into the diffusion. This problem has been open since [J. Yong, Stochastic Process Appl. 116 (2006) 779–795] obtained the analogue result for the case of convex control region. The key is to introduce a pair of suitable second-order adjoint processes (SOAPs). It is found that the usual way of using only one SOAP in the maximum condition for the classical setting of controlled stochastic differential equations does not work here.
Mathematics Subject Classification: 93E20 / 60H20 / 49K45
Key words: Stochastic Volterra integral equations / maximum principles / second-order adjoint processes / non-convex control region
© EDP Sciences, SMAI 2020
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