Designing an expert knowledge-based Systemic Importance Index for financial institutions

Defining whether a financial institution is systemically important (or not) is challenging due to (i) the inevitability of combining complex importance criteria such as institutions’ size, connectedness and substitutability; (ii) the ambiguity of what an appropriate threshold for those criteria may be; and (iii) the involvement of expert knowledge as a key input for combining those criteria. The proposed method, a Fuzzy Logic Inference System, uses four key systemic importance indicators that capture institutions’ size, connectedness and substitutability, and a convenient deconstruction of expert knowledge to obtain a Systemic Importance Index. This method allows for combining dissimilar concepts in a non-linear, consistent and intuitive manner, whilst considering them as continuous –non binary- functions. Results reveal that the method imitates the way experts them-selves think about the decision process regarding what a systemically important financial institution is within the financial system under analysis. The Index is a comprehensive relative assessment of each financial institution’s systemic importance. It may serve financial authorities as a quantitative tool for focusing their attention and resources where the severity resulting from an institution failing or near-failing is estimated to be the greatest. It may also serve for enhanced policy-making (e.g. prudential regulation, oversight and supervision) and decision-making (e.g. resolving, restructuring or providing emergency liquidity).Systemic Importance, Systemic Risk, Fuzzy Logic, Approximate Reasoning, Too-connected-to-fail, Too-big-to-fail. Classification JEL: D85, C63, E58, G28.

Investments in Social Ties, Risk Sharing and Inequality

This paper investigates stable and efficient networks in the context of risk-sharing, when it is costly to establish and maintain relationships that facilitate risk-sharing. We find a novel trade-off between efficiency and equality. The most stable effic

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

On the topology Of network fine structures

Multi-relational dynamics are ubiquitous in many complex systems like transportations, social and biological. This thesis studies the two mathematical objects that encapsulate these relationships --- multiplexes and interval graphs. The former is the modern outlook in Network Science to generalize the edges in graphs while the latter was popularized during the 1960s in Graph Theory. Although multiplexes and interval graphs are nearly 50 years apart, their motivations are similar and it is worthwhile to investigate their structural connections and properties. This thesis look into these mathematical objects and presents their connections. For example we will look at the community structures in multiplexes and learn how unstable the detection algorithms are. This can lead researchers to the wrong conclusions. Thus it is important to get formalism precise and this thesis shows that the complexity of interval graphs is an indicator to the precision. However this measure of complexity is a computational hard problem in Graph Theory and in turn we use a heuristic strategy from Network Science to tackle the problem. One of the main contributions of this thesis is the compilation of the disparate literature on these mathematical objects. The novelty of this contribution is in using the statistical tools from population biology to deduce the completeness of this thesis's bibliography. It can also be used as a framework for researchers to quantify the comprehensiveness of their preliminary investigations. From the large body of multiplex research, the thesis focuses on the statistical properties of the projection of multiplexes (the reduction of multi-relational system to a single relationship network). It is important as projection is always used as the baseline for many relevant algorithms and its topology is insightful to understand the dynamics of the system.Open Acces

Financial stability from a network perspective

This thesis consists of six chapters related to applications of network analysis’ methods for financial stability. The first chapter introduces the network perspective as a new mapping technique for studying and understanding financial markets’architecture. The second chapter breaks down the Colombian sovereign securities market into different layers of interaction corresponding to distinct trading and registering platforms. The third chapter addresses an overlooked issue: How to measure the importance of financial market infrastructures within their corresponding network. The fourth chapter studies the connective and hierarchical structure of the Colombian non-collateralized money market, and uses an information retrieval algorithm for identifying those financial institutions that simultaneously excel at borrowing and lending central bank’s liquidity (i.e. superspreaders). The fifth chapter addresses –for the first time- the question regarding the presence of a modular hierarchy in financial networks, and discusses the main implications for financial stability. The sixth chapter explicitly models the role of financial market infrastructures as financial markets’ “plumbing”, and recognizes that traditional analysis of financial institutions networks is of a virtual or logical nature. The third chapter is published in the Journal of Financial Market Infrastructures (Vol.2 (3), 2014), whereas the fourth chapter is published in the Journal of Financial Stability (Vol.15, 2014)