一、个人简介
李小娟，女，博士，毕业于山东大学中泰证券金融研究院。研究方向为随机最优控制理论和非线性期望理论。在国际重要学术期刊SIAM Journal on Control and Optimization 、Transactions of the American Mathematical Society、Science China - Mathematics等发表SCI论文十余篇。主持并参与山东省自然科学基金、国家自然科学基金项目多项。
二、研究方向
1.随机最优控制
2.非线性期望
三、学术兼职
山东省大数据研究会理事
四、开设课程
数学分析
五、科研项目
1.山东省自然科学基金项目：g-期望和G-期望中的几个问题，第1位，主持
2.山东省自然科学基金项目：基于信息粒化和知识指导的区间值时间序列的聚类研究，第2位
2.国家自然科学基金项目：区间值时序数据挖掘中聚类与预测的研究，第5位
六、代表性成果
1. Xiaojuan Li, Mingshang Hu, Maximum principle for stochastic optimal control problem under convex expectation, SIAM Journal on Control and Optimization 63(1), 524-545, (2025), (SCI)
2. Mingshang Hu, Shaolin Ji, Xiaojuan Li (通讯), BSDEs driven by G-Brownian motion under degenerate case and its application to the regularity of fully nonlinear PDEs, Transactions of the American Mathematical Society 377(5), 3287–3323, (2024), (SCI)
3. Xiaojuan Li, Some properties of g-convex functions. Science China-Mathematics 56(10), 2117–2122, (2013),（SCI）
4. Mingshang Hu, Shaolin Ji, Xiaojuan Li (通讯), Dynamic programming principle and Hamilton-Jacobi-Bellman equation under nonlinear expectation, ESAIM: Control Optimisation and Calculus of Variations 28:1–21, (2022), (SCI)
5. Xiaojuan Li, Dynamic programming principle for stochastic optimal control problem under degenerate G-expectation, Systems & Control Letters 196, 1-10, (2025),（SCI）
6. Xiaojuan Li, Relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problem under volatility uncertainty, Optimal Control Applications and Methods, 2457-2475, (2023), (SCI)
7. Xiaojuan Li, Forward-backward stochastic differential equations driven by G-Brownian motion under weakly coupling condition, Journal of Mathematical Analysis and Applications 526, 1-19, (2023), (SCI)
8. Xiaojuan Li, Xinpeng Li, On the capacity for degenerated G-Brownian motion and its application, Electronic Communication in Probability 28, 1–9, (2023), (SCI)
9. Xiaojuan Li, On the integral representation of g-expectations with terminal constraints, Journal of Mathematical Analysis and Applications 452, 16–26, (2017), (SCI)
10. Mingshang Hu, Xiaojuan Li, Independence Under the G-Expectation Framework, Journal of Theoretical Probability 27, 1011–1020, (2014), (SCI)
11. Mingshang Hu, Xiaojuan Li, Xinpeng Li, Convergence rate of Peng’s law large numbers under sublinear expectations, Probability, Uncertainty and Quantitative Risk 6, 261-266, (2021).
