题目：Stochastic Indefinite Partially Observed Large-population Problem

摘要：We investigate an indefinite linear-quadratic partially observed large-population problem with common noise, where both the state-average and control-average are considered. All weighting matrices in the cost functional can be indefinite. We obtain the decentralized optimal strategies by the Hamiltonian approach and demonstrate the well-posedness of Hamiltonian system by virtue of relaxed compensator. The related Consistency Condition and the feedback form of decentralized optimal strategies are derived. Moreover, we prove that the decentralized optimal strategies are $\varepsilon$-Nash equilibrium by using the relaxed compensator.

个人简介：聂天洋，山东大学数学学院教授，副院长。研究方向为倒向随机微分方程、随机控制、金融数学。主持国家基金委优秀青年基金、国家重点研发计划课题等项目。曾获山东省自然科学奖、山东省青年科技奖等。

时间地点：11月12号 14：30-16：00 腾讯会议 544-543-296

题目：BSDEs driven by G-Brownian motion under degenerate case and its application to the regularity of fully nonlinear PDEs

摘要：We obtain the existence and uniqueness theorem for backward stochastic differential equation driven by G-Brownian motion (G-BSDE) under degenerate case. Moreover, we propose a new probabilistic method based on the representation theorem of G-expectation and weak convergence to obtain the regularity of fully nonlinear PDE associated to G-BSDE. This is a joint work with Shaolin Ji and Xiaojuan Li.

个人简介: 胡明尚，山东大学中泰证券金融研究院教授，博士生导师，山东省泰山学者青年专家。主要研究方向为非线性期望、倒向随机微分方程、随机控制、金融数学等。在Transactions of the American Mathematical Society, SIAM Journal on Control and Optimization, Stochastic Processes and their Applications, Journal of Differential Equations 等杂志发表论文30余篇。近年来，主持国家自然科学基金数学天元基金重点专项1项，主持完成国家自然科学基金面上项目1项。

时间地点：11月18号 9：00-10：30 腾讯会议 348-616-849

题目：Optimal State Equation for the Control with Two Distinct Dynamic Systems

摘要：We consider a class of stochastic control problems which have been widely used in optimal foraging theory and financial modeling. The optimal state process has two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether it takes values bigger or smaller than a threshold value. Adopting a perturbation type approach, we find an expression for potential measure of the optimal state process. We then obtain an expression for the transition density of the optimal state process by inverting the associated Laplace transform. Properties including the stationary distribution of the optimal state process are discussed. Finally, the expression of the value function is given for such stochastic control problems.

个人简介: 吴盼玉，山东大学中泰证券金融研究院教授，2020年入选山东大学青年学者未来计划。主要从事非线性概率与期望、倒向随机微分方程理论及应用、金融数学等领域的研究。在Stoch. Proc. Appl.，Automatica，Sci. China Math.等国内外知名期刊上发表学术论文近二十篇。主持国家自然科学基金、山东省自然科学基金、博士后基金等多项科研项目，作为骨干成员参加国家重点研发计划以及山东省自然科学基金重大基础研究项目。曾获山东省高等学校科学技术奖二等奖。

时间地点：11月12号 10：30-12：00 腾讯会议 248-280-030