报告题目：Data-driven Distributionally Robust Multiproduct Pricing Problems under Pure Characteristics Demand

报告人：孙海琳教授、博导，南京师范大学

报告时间：2023年10月20日下午15:15—16:15

报告地点：数理楼306

报告对象：感兴趣的教师、研究生、本科生等

主办单位：beat365

报告人简介：孙海琳博士是南京师范大学数学科学学院教授、博士生导师。他于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。在其博士期间，他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。他的研究领域包括随机优化，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。他在包括《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。

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.