题    目：Data-driven Distributionally Robust Multiproduct Pricing Problems under Pure Characteristics Demand

主讲人：孙海琳 教授

单    位：南京师范大学

时    间：2024年11月8日11：00

地    点：郑州校区九章学堂C座302

摘    要：This paper considers a multiproduct pricing problem under pure characteristics demand and the ambiguity of the true probability distribution. We formulate this problem as a distributionally robust optimization (DRO) problem based on a constructive approach to estimating pure characteristics demand models with pricing by Pang, Su and Lee. We show that the DRO problem is well-defined, and the objective function is upper semicontinuous by using an equivalent hierarchical form and the sparse solution in the consumers' purchase decision problem. We also analyze the data-driven approach when the ambiguity set is given by a general moment-based case. We give convergence results as the data size tends to infinity and analyze the quantitative statistical robustness in view of the possible contamination of driven data. Furthermore, we use the Lagrange duality to reformulate the DRO problem as a mathematical program with complementarity constraints, and give a numerical procedure for finding a global solution of the DRO problem under certain specific settings. Finally, we report numerical results that validate the effectiveness of our approach for the distributionally robust multiproduct pricing problem.

简    介：孙海琳，博士，南京师范大学数学科学学院教授。2007 年在吉林大学获得统计学学士学位，2013 年毕业于哈尔滨工业大学，获数学博士学位。其博士期间，在英国南安普顿大学和香港理工大学联合培养。2015-2017 年在香港理工大学应用数学系做博士后研究。2018 年获中国运筹学会青年科技奖和江苏省数学成就奖，主持国家自然科学基金优秀青年科学基金项目、面上项目和青年科学基金项目。研究领域：随机优化，分布鲁棒优化、随机变分不等式及其在投资组合、风险管理和经济学模型上的应用。在《Mathematical Programming》、《SIAM Journal on Optimization》、《Mathematics of Operations Research》等国际权威期刊发表了二十多篇论文，担任《运筹学学报》、《计算数学》、《Journal of Optimization Theory and Applications》、《Asia-Pacific Journal of Operational Research》、 《Numerical Algebra, Control and Optimization》等期刊编委。