报告人：张帅琪（中国矿业大学）

时  间：8月2日下午14:30

地  点：腾讯会议ID：842 177 651（无设置密码）

内容摘要:

This talk deals with optimal stochastic control problem for stochastic differential equation driven by sub-diffusion. We develop stochastic maximum principles using both spike and convex variational method separately. The existence and uniqueness of the adjoint equation which is a backward stochastic differential equation driven by sub-diffusion is proved. Two versions of sufficient condition with and without assumption of the concavity of the Hamiltonian is given, which are corresponding to the spiking and convex variation, respectively. Moreover, a dynamic programing principle (DPP) is studied. We want to emphasize that sub-diffusion process is not Markov. In order to put it into DPP setting, we add overshot process to make it Markovian. Because of sub-diffusion, the Hamilton-Jacobi-Bellman (HJB) equation contains fractional derivative. Also, its connections to the adjoint process is established. These results are applied to two examples including a linear quadratic problem and a mean-variance portfolio selection problem. Both of them are solved explicitly. Last but not least, we compare the control of diffusion and that of sub-diffusion not only theoretically but also by numerical simulation.

个人简介：

张帅琪，中国矿业大学数学学院副教授，2012年毕业于中南大学，获理学博士学位，澳门大学大学博士后，美国数学会特邀评论员。主要从事随机控制，非线性滤波，保险精算领域的研究。迄今在控制领域顶级刊物SIAM J. Control Optim, Systms Control Lett.在精算领域顶级期刊Scand. Actuar. J.，中国科学:数学，中国科学：信息科学，Appl, Math.Compt.等刊物发表学术论文20余篇。

联系人：王文元