报告地点：行健楼学术活动室526
邀请人：蔡邢菊教授
报告摘要：We consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process that involves both transition of system states and dynamic change of the stochastic environment affected respectively by potential endogenous uncertainties and exogenous uncertainties. The generality of the proposed model is illustrated through several examples. After deriving nested reformulation of the problem, we discuss the continuity, Lipschitz continuity and convexity of the stage-wise optimal value functions. Then we carry out quantitative stability analysis of the model in terms of the optimal value and the set of optimal solutions under the perturbation of the probability distributions of the endogenous uncertainty and the exogenous uncertainty. Specifically, we quantify the effects of the perturbation of the two uncertainties on the optimal values and optimal solutions by deriving the error bounds in terms of Kantorovich metric and Fortet-Mourier metric of the probability distributions of the respective uncertainties. These results differ from the existing stability results established in terms of the filtration distance or the nested distance.
报告人简介：
陈志平，国家天元数学西北中心副主任，西安交通大学二级教授、博士生导师；长期从事随机规划理论及其应用、分布鲁棒优化、强化学习、金融风险度量、保险精算与投资分析等领域的学术研究，在SIAM J. Optim., Math. Oper. Res., Math. Program., Eur. J. Oper. Res., J. Bank. Finance, J. Econ. Dyn. Control, Insur. Math. Econ.等运筹学、经济与金融领域学术期刊发表SCI（SSCI）检索论文120余篇；先后主持国家自然科学基金项目及横向项目20余项，现主持国家重点研发计划重点专项“强化学习的数学理论与随机优化的自学习方法”；现任《OR Spectrum》、《Big Data and Information Analytics》、《Mathematics》、《西安交通大学学报》、《工程数学学报》等国内外期刊的编委；现任中国运筹学会常务理事，中国优选法统筹法与经济数学研究会量化金融与保险分会常务理事，中国管理科学与工程学会金融计量与风险管理研究会理事，中国管理科学与工程学会理事，中国工业与应用学学会竞赛工作委员会委员等。
