Essays on Applications of Networks and Discrete Optimization

Abstract

This dissertation examines novel applications of network and discrete optimization models in three settings: 1) a social network analysis of stock prices; 2) personnel planning for large, client-centric service organizations; and 3) identifying regimes in financial time series by formal discrete quadratic programming models. In each case, the overall purpose is to improve performance as compared with traditional techniques, while addressing practical concerns regarding data and solution constraints. The first chapter presents a graphical network approach for analyzing the temporal structure of financial markets with a focus on temporal stock price movements. Three unsupervised learning algorithms are linked to construct the network over several time periods. A derived investment strategy generate performance with lower volatility than alternative strategies. The resulting graphs give insights into the dynamic patterns in stock prices relative to each other and to the market. The second chapter introduces a flexible personnel planning framework for large service sector organizations with a client-centric focus, such as concierge banks and wealth management firms. The approach is to approximate the problem as a two-stage network optimization model, rather than solving an integer linear program for the full organization. We demonstrate that the network approach provides a practical and flexible tool for decisions involving assigning the key bank employees to clients. In particular, the model improves efficiency by reducing superfluous connections while maintaining a balanced workload and importantly, generating a higher quality-of-service for the firm’s clients. The system is designed to allow a close interaction between the decision makers and the network optimization solver. The third chapter investigates the discovery of regimes in financial markets by means of the recent research on non-parametric jump models. Rather than solving the jump model with a heuristic combination of the k-means clustering algorithm and dynamic programming (a type of coordinate decent), we construct a formal discrete quadratic program and develop a candidate driven approximate approach. Here the candidate model greatly improves solution efficiency, while generating solutions that are close to the jump model. Applications of the proposed model are shown in both the case of the discrete and the continuous jump models.