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Systemic risk is the risk that an economic shock may result in the breakdown of the fundamental functions of the financial system. It can involve multiple vectors of infection such as chains of losses or consecutive failures of financial institutions that may ultimately cause the failure of the financial system to provide liquidity, stable prices, and to perform economic activities. This thesis develops methods to quantify systemic risk, its effect on the financial system and perhaps more importantly, to determine its cause. In the first chapter, we provide an overview and a literature review of the topics covered in this thesis. First, we present a literature review on network-based models of systemic risk. Finally we end the first chapter with a review on market impact models. In the second chapter, we consider one unregulated financial institution with constant absolute risk aversion investment risk preferences that optimizes its strategies in a multi asset market impact model with temporary and permanent impact. We prove the existence and derive explicitly the optimal trading strategies. Furthermore, we conduct numerical exploration on the sensitivity of the optimal trading curve. This chapter sets the foundation for further research into multi-agent models and systemic risk models with optimal behaviours. In the third chapter, we extend the market impact models to the multi-agent setting. The agents follow a game theoretic strategy that is constrained by the regulations imposed. Furthermore, the agents must liquidate themselves if they become insolvent or unable to meet the regulations imposed on them. This paper provides a bridge between market impact models and network models of systemic risk. In chapter four, we introduce a financial network model that combines the default and liquidity stress mechanisms into a ``double cascade mapping''. Unlike simpler models, this model can quantify how illiquidity or default of one bank influences the overall level of liquidity stress and default in the system. We derive large-network asymptotic cascade mapping formulas that can be used for efficient network computations of the double cascade. Finally we use systemic risk measures to compare the results of including with and without an asset firesale mechanism. / Thesis / Doctor of Philosophy (PhD)

Recommender systems automate the process of recommending products and services to customers based on various types of data including customer demographics, product features, and, most importantly, previous interactions between customers and products (e.g., purchasing, rating, and catalog browsing). Despite significant research progress and growing acceptance in real-world applications, two major challenges remain to be addressed to implement effective e-commerce recommendation applications. The first challenge is concerned with making recommendations based on sparse transaction data. The second challenge is the lack of a unified framework to integrate multiple types of input data and recommendation approaches.This dissertation investigates graph-based algorithms to address these two problems. The proposed approach is centered on consumer-product graphs that represent sales transactions as links connecting consumer and product nodes. In order to address the sparsity problem, I investigate the network spreading activation algorithms and a newly proposed link analysis algorithm motivated by ideas from Web graph analysis techniques. Experimental results with several e-commerce datasets indicated that both classes of algorithms outperform a wide range of existing collaborative filtering algorithms, especially under sparse data. Two graph-based models that enhance the simple consumer-product graph were proposed to provide unified recommendation frameworks. The first model, a two-layer graph model, enhances the consumer-product graph by incorporating the consumer/product attribute information as consumer and product similarity links. The second model is based on probabilistic relational models (PRMs) developed in the relational learning literature. It is demonstrated with e-commerce datasets that the proposed frameworks not only conceptually unify many of the existing recommendation approaches but also allow the exploitation of a wider range of data patterns in an integrated manner, leading to improved recommendation performance.In addition to the recommendation algorithm design research, this dissertation also employs the random graph theory to study the topological characteristics of consumer-product graphs and the fundamental mechanisms that generate the sales transaction data. This research represents the early step towards a meta-level analysis framework for validating the fundamental assumptions made by different recommendation algorithms regarding the consumer-product interaction generation process and thus supporting systematic recommendation model/algorithm selection and evaluation.

abstract: The cyber-physical systems (CPS) are emerging as the underpinning technology for major industries in the 21-th century. This dissertation is focused on two fundamental issues in cyber-physical systems: network interdependence and information dynamics. It consists of the following two main thrusts. The first thrust is targeted at understanding the impact of network interdependence. It is shown that a cyber-physical system built upon multiple interdependent networks are more vulnerable to attacks since node failures in one network may result in failures in the other network, causing a cascade of failures that would potentially lead to the collapse of the entire infrastructure. There is thus a need to develop a new network science for modeling and quantifying cascading failures in multiple interdependent networks, and to develop network management algorithms that improve network robustness and ensure overall network reliability against cascading failures. To enhance the system robustness, a "regular" allocation strategy is proposed that yields better resistance against cascading failures compared to all possible existing strategies. Furthermore, in view of the load redistribution feature in many physical infrastructure networks, e.g., power grids, a CPS model is developed where the threshold model and the giant connected component model are used to capture the node failures in the physical infrastructure network and the cyber network, respectively. The second thrust is centered around the information dynamics in the CPS. One speculation is that the interconnections over multiple networks can facilitate information diffusion since information propagation in one network can trigger further spread in the other network. With this insight, a theoretical framework is developed to analyze information epidemic across multiple interconnecting networks. It is shown that the conjoining among networks can dramatically speed up message diffusion. Along a different avenue, many cyber-physical systems rely on wireless networks which offer platforms for information exchanges. To optimize the QoS of wireless networks, there is a need to develop a high-throughput and low-complexity scheduling algorithm to control link dynamics. To that end, distributed link scheduling algorithms are explored for multi-hop MIMO networks and two CSMA algorithms under the continuous-time model and the discrete-time model are devised, respectively. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012

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