CAREER: Optimal Design, Policy and Risk Management of Central Nodes in Stochastic Networks

这项教师早期职业发展（Career）奖的目标是开发一个全面的框架，用于设计和优化具有中心控制节点的星形随机网络的资源分配。中心节点通过汇集每个单独节点的部分资源并承保低于阈值的节点来管理系统风险。这个项目将推进运筹学和随机分析的方法论。这种系统出现在许多情况下，包括分布式零售业务，其中资源是商品库存，允许延期订购，以及金融网络，其中资源是现金和其他资本资产，单个节点可能会出现现金短缺。该教育计划将通过与女高中生进行为期一周的有组织的外展活动，以及在年度全国会议上为初级女性研究人员举办与风险管理和金融行业的高级女性管理人员互动的特别会议，扩大女性在STEM领域的参与。将中心节点和单个节点的资源建模为多维标记点过程，并对首次通过时间进行表征和研究。在合作博弈论环境下，通过考虑单个节点的随机行为来确定每个节点对池中心节点的最优贡献，并研究这些博弈的纳什均衡。中心节点具有独立的布朗分量的情况下，可以增强系统的运行也将被考虑。开发的模型将根据现有数据进行校准。

The goal of this Faculty Early Career Development (CAREER) award is to develop a comprehensive framework for the design of and optimal resource allocation in star-shaped stochastic networks with a central control node. The central node serves to manage system risk by pooling a portion of the resources of each individual node and underwriting a node that falls below a threshold value. This project will advance methodologies in both operations research and stochastic analysis. Such systems arise in many contexts, including distributed retail operations, where resources are inventories of goods and backordering is allowed, and financial networks, where resources are cash and other capital assets and individual nodes may experience cash shortfalls. The education plan will broaden participation of females in STEM fields through a structured week-long outreach activity with female high school students and by organizing special sessions for junior female researchers to interact with senior female executives in the risk management and financial industry at an annual national conference. Resources of the central node and individual nodes are modeled as multidimensional marked point processes, and first passage times are characterized and studied. Optimal contributions from each node to the pooled central node are determined by considering individual nodes' stochastic behavior in a cooperative game-theoretic setting, and the Nash equilibrium of these games will be studied. The case where the central node has an independent Brownian component that can enhance system operation will be also be considered. The developed models will be calibrated with available data.