Complexity and Multilayer Networks in Economics and Finance

Begeleiding : Prof. Koen Schoors (promotor, Faculteit Economie en Bedrijfskunde), Jan Ryckebusch (promotor), Benjamin Vandermarliere, Andres Belaza, Milan van den Heuvel, Ken Bastiaensen )
General context
One of fhe most puzzling things about the financial crisis of 2008 is that it was caused by a relatively small group of financial products. The subprime exposure, which was often believed to be rather marginal, gave rise to widespread problems, and started a domino effect which made the entire financial system to topple. In physicist's jargon, this means that a local perturbation affected the system as a whole. This was possible because over the years, the financial system grew more and more complex. Thereby, all agents in the financial system are highly interconnected very by means of unrecognized links. Policy makers tried to stabilize the system by devising rules for each individual player. In physics it is well known that "The whole is most often more than the sum of its parts", and systemic risk is also at play in the highly interconnected financial system.
The financial calamities of 2008 has boosted a lot research into the complexity of interbank networks in particular, and in economics and finance in general. This field is highly interdisciplinary drawing on big data manipulation, advanced statistical analyses, computational sciences, finance, game theory, network theory and complexity science. We propose two master's thesis subjects in a timely and very exciting field of interdisciplinary Physics.

Subject 1: Controllability in interbank networks
The application of network theory to interbank systems already resulted in major advances in our understanding about their topology, interaction dynamics, and growth. A major issue is the endeavour to steer the evolution of the banking system in the direction of optimized control. Thereby, one aims at defining the rules of the operation of the interbank credit system such that it evolves in a certain direction.
The master's thesis will address the issue of structural controllability of interbank credit networks under different conditions. Using principles of network theory one can identify the nodes which need to be controlled in order to achieve a status whereby one can drive the network from an initial state to a selected final state. Thereby, it is essential to possess an effective method or algorithm to identify the driver nodes at each instant of time.
Controllability in network science is a relatively new theory. After having mastered the concept of controllablity, the student will study a version of the CRISIS agent-based interbank model. She/he will analyse the time series of the evolution of the interbank system under different scenarios. In particular, a study will be made of the connection between controllability and the underlying dynamics of the simulated network. The concept of control very much hinges on the (non)existence of a link between different nodes in the network. Traditionally, interactions between nodes are aggregated into a single network layer. In practice, interactions can adopt very different forms and some interactions may be more effective than others to gain control of the nodes. To this end, one has developed the concepts of multilayer networks ( A recent paper on the topic of Multilayer Networks ). In the context of the research for the master's thesis, it will be investigated whether the theory of Multilayer Networks provides a superior way of defining the controllability of the system.
Subject 2: Discrete Scale Invariance and Exchange-traded funds
An exchange-traded fund (ETF) is a fairly new financial product which enables investors to easily own and trade a share of large and well-diversified portfolios. In the total net assets distribution of these ETFs we have found indications of discrete scale invariance (DSI). The first goal of this thesis will be to analyze rigorously whether there actually is DSI or not, where the student will implement the Lomb diagram technique. The second goal of the thesis, if the DSI hypothesis is confirmed, will be to understand and model the underlying mechanism.

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