In this article, a class of backward stochastic Volterra integro-differential equations (BSVIDEs) is introduced and studied. It is worthy mentioning that the proposed BSVIDEs can not be covered by the existing backward stochastic Volterra integral equations (BSVIEs), and they also have the nice flow property such that Ito's formula becomes quite applicable. It is found that BSVIDEs can provide a neat sufficient condition for the solvability of BSVIEs with generator depending on the diagonal value of the solutions. As applications, the optimal control problems in terms of maximum principles and linear quadratic control problems of optimal control for forward stochastic Volterra integro-differential equations (FSVIDE) are investigated. In contrast with the BSVIEs in current literature, some interesting phenomena and advantages of BSVIDEs are revealed.

报告人简介

王天啸，四川大学数学学院副教授、博士研究生导师。主要从事随机分析，随机最优控制理论等方面的研究。曾赴美国中佛罗里达大学、堪萨斯大学、香港理工大学等知名高校访问交流。主持和参与多项国家自然科学基金青年项目、面上项目与重点项目。发表论文涉及《 SIAM J. Control Optim.》, 《IEEE Trans. Automat. Control》,《ESAIM: Control Optim. Calc. Var.》,《Appl. Math. Optim.》,《Insurance: Math. Econom.》,《Stochastic Process Appl.》等杂志。