Modern financial networks are complicated structures that can contain multiple types of nodes and connections between those nodes. Banks, governments and even individual people weave into an intricate network of debt, risk correlations and many other forms of interconnectedness. We explore multiple types of financial network models with a focus on understanding the dynamics and causes of cascading failures in such systems. In particular, we apply real-world data from multiple sources to these models to better understand real-world financial networks. We use the results of the Federal Reserve "Banking Organization Systemic Risk Report" (FR Y-15), which surveys the largest US banks on their level of interconnectedness, to find relationships between various measures of network connectivity and systemic risk in the US financial sector. This network model is then stress-tested under a number of scenarios to determine systemic risks inherent in the various network structures. We also use detailed historical balance sheet data from the Venezuelan banking system to build a bipartite network model and find relationships between the changing network structure over time and the response of the system to various shocks. We find that the relationship between interconnectedness and systemic risk is highly dependent on the system and model but that it is always a significant one. These models are useful tools that add value to regulators in creating new measurements of systemic risk in financial networks. These models could be used as macroprudential tools for monitoring the health of the entire banking system as a whole rather than only of individual banks.

Yes / Amid its rapidly increasing usage and immense public interest the subject of Bitcoin has raised profound economic and societal issues. In this paper we undertake economic and econometric modelling of Bitcoin prices. As with many asset classes we show that Bitcoin exhibits speculative bubbles. Further, we find empirical evidence that the fundamental price of Bitcoin is zero.

1 Title: Statistical Physics of Frustrated Evolutionary Games Author: Miroslav Pištěk Department: Institute of Theoretical Physics Supervisor: RNDr. František Slanina, CSc. Supervisor's e-mail address: slanina@fzu.cz Abstract: In last two decades, the effort devoted to interdisciplinary research of bounded sources allocation is growing, examining complex phenomena as stock markets or traffic jams. The Minority Game is a multiple-agent model of inevitable frus- tration arising in such situations. It is analytically tractable using the replica method originated in statistical physics of spin glasses. We generalised the Mi- nority Game introducing heterogenous agents. This heterogeneity causes a con- siderable decrease of an average agent's frustration. For many configurations, we achieve even a positive-sum game, which is not possible in the original game variant. This result is in accordance with real stock market data. Keywords: frustrated evolutionary games, Minority Game, Replica method

Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex microstructure effects to develop high-performance materials, but general microstructure quantification is an unsolved problem. Motivated by statistical physics, I envision microstructure as a low-dimensional manifold, and construct this manifold by leveraging multiple machine learning approaches including transfer learning, dimensionality reduction, and computer vision breakthroughs with convolutional neural networks.

This dissertation covers the two major parts of my Ph.D. research: i) developing theoretical framework of complex networks; and ii) applying complex networks models to quantitatively analyze economics systems. In part I, we focus on developing theories of interdependent networks, which includes two chapters: 1) We develop a mathematical framework to study the percolation of interdependent networks under targeted-attack and find that when the highly connected nodes are protected and have lower probability to fail, in contrast to single scale-free (SF) networks where the percolation threshold pc\ = 0, coupled SF networks are significantly more vulnerable with pc\ significantly larger than zero. 2) We analytically demonstrate that clustering, which quantifies the propensity for two neighbors of the same vertex to also be neighbors of each other, significantly increases the vulnerability of the system. In part II, we apply the complex networks models to study economics systems, which also includes two chapters: 1) We study the US corporate governance network, in which nodes representing directors and links between two directors representing their service on common company boards, and propose a quantitative measure of information and influence transformation in the network. Thus we are able to identify the most influential directors in the network. 2) We propose a bipartite networks model to simulate the risk propagation process among commercial banks during financial crisis. With empirical bank's balance sheet data in 2007 as input to the model, we find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation during the financial crisis between 2008 and 2011. The results suggest that complex networks model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008 - 2011.

Yes / We develop bespoke rational bubble models for Bitcoin and cryptocurrencies that incorporate both heavy tails and the probability of a complete collapse in asset prices. Empirically, we present robustified evidence of bubbles in Bitcoin and Ethereum. Theoretically, we show that liquidity risks may generate heavy-tails in Bitcoin and cryptocurrency markets. Even in the absence of bubbles dramatic booms and busts can occur. We thus sound a timely note of caution.

Yes / In this paper we draw upon the close relationship between statistical physics and mathematical finance to develop a suite of models for financial bubbles and crashes. The derived models allow for a probabilistic and statistical formulation of econophysics models closely linked to mainstream financial models. Applications include monitoring the stability of financial systems and the subsequent policy implications. We emphasise the timeliness of our contribution with an application to the two largest cryptocurrency markets: Bitcoin and Ripple. Results shed new light on emerging debates over the nature of cryptocurrency markets and competition between rival digital currencies.

The paper deals with quantum economy. It means the methods of quantum mechanics are applied in the study of economic processes. The scalar abstract economic quantities are constructed as follows: general abstract economic quantity F , average abstract economic quantity FA, marginal abstract economic quantity FM, marginal average abstract economic quantity FMA, average marginal abstract economic quantity FAM, elasticity of abstract economic quantity EF. All the abstract economic quantities mentioned above are constructed as mappings. The general theory of abstract economic quantities is utilized in a construction of the abstract total gross profit TGP. The set of static models of total gross profit TGP is constructed in the case that the first unit gross profit is slowly changed with time while the second unit gross profit is quickly changed with time in comparison with the first unit gross profit.

For financial forcasting of crisis new concepts from disciplines dissimilar to economics are looked for by financial experts. The branch of econophysics using theories of natural sciences is significant. The meaning of this work is to point out one of many methods applied to financial data with help of the theory of turbulence of fluids and deterministic chaos. We provide a parallel analysis of high frequency financial time series of a stock index and velocities of a turbulent fluid. This work concerns the use of concepts from statistical mathematics, probability theory and scaling. We find differences of both studied systems but the methodologies of natural diciplines can be also applied to financial data.

abstract: This dissertation examines six different models in the field of econophysics using interacting particle systems as the basis of exploration. In each model examined, the underlying structure is a graph G = (V , E ), where each x ∈ V represents an individual who is characterized by the number of coins in her possession at time t. At each time step t, an edge (x, y) ∈ E is chosen at random, resulting in an exchange of coins between individuals x and y according to the rules of the model. Random variables ξt, and ξt(x) keep track of the current configuration and number of coins individual x has at time t respectively. Of particular interest is the distribution of coins in the long run. Considered first are the uniform reshuffling model, immediate exchange model and model with saving propensity. For each of these models, the number of coins an individual can have is nonnegative and the total number of coins in the system is conserved for all time. It is shown here that the distribution of coins converges to the exponential distribution, gamma distribution and a pseudo gamma distribution respectively. The next two models introduce debt, however, the total number of coins again remains fixed. It is shown here that when there is an individual debt limit, the number of coins per individual converges to a shifted exponential distribution. Alternatively, when a collective debt limit is imposed on the whole population, a heuristic argument is given supporting the conjecture that the distribution of coins converges to an asymmetric Laplace distribution. The final model considered focuses on the effect of cooperation on a population. Unlike the previous models discussed here, the total number of coins in the system at any given time is not bounded and the process evolves in continuous time rather than in discrete time. For this model, death of an individual will occur if they run out of coins. It is shown here that the survival probability for the population is impacted by the level of cooperation along with how productive the population is as whole. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019