Backward doubly stochastic Volterra integral equations and applications to optimal control problems
Probability
2019-06-26 v1 Optimization and Control
Abstract
Backward doubly stochastic Volterra integral equations (BDSVIEs, for short) are introduced and studied systematically. Well-posedness of BDSVIEs in the sense of introduced M-solutions is established. A comparison theorem for BDSVIEs is proved. By virtue of the comparison theorem, we derive the existence of solutions for BDSVIEs with continuous coefficients. Furthermore, a duality principle between linear (forward) doubly stochastic Volterra integral equation (FDSVIE, for short) and BDSVIE is obtained. A Pontryagin type maximum principle is also established for an optimal control problem of FDSVIEs.
Cite
@article{arxiv.1906.10582,
title = {Backward doubly stochastic Volterra integral equations and applications to optimal control problems},
author = {Yufeng Shi and Jiaqiang Wen and Jie Xiong},
journal= {arXiv preprint arXiv:1906.10582},
year = {2019}
}