时 间：2024-12-19 09:30 - 11:00
地 点：普陀校区理科大楼A1714
报告人：张霜剑 复旦大学青年研究员
主持人：李丹萍 华东师范大学教授
摘 要：
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures on the marginal spaces, but the joint nonadditive distribution on the product space is unknown. We treat this problem as a generalization of the optimal transportation problem to the setting of nonadditive measures. We provide explicit characterizations of the optimal solutions for finite marginal spaces, and we investigate some of their properties. We further discuss the connections with linear programming, showing that the optimal transport problems for capacities are linear programs, and we also characterize their duals explicitly. This is joint work with David Saunders and Mario Ghossoub.
报告人简介：
张霜剑，复旦大学数学科学学院青年研究员，博士生导师，国家高层次青年人才。2023年9月至今任职于复旦大学数学科学学院，研究方向为最优输运理论在经济金融中的应用，在垄断定价等领域取得重要研究成果。其研究成果发表在Communications on Pure and Applied Mathematics、Mathematical Models and Methods in Applied Sciences、Economic Theory、Journal of Mathematical Economics、Conference on Learning Theory等。