Acronym:

Algorithms for Systemic Risk Measurement 

From: 2015-10-01 To: 2018-09-30 (Completed)

HRZZ 

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doc.dr.sc. Zvonko Kostanjčar

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Consider a complex system (such as a nuclear plant) that is made from many subsystems which themselves have certain probabilities of failure, and these probabilities are not independent. Suppose that we are interested in the probability of failure of the entire system, failure that occurs when certain subset of the subsystems fail, i.e. we are interested in the systemic risk. How do we model such a situation and estimate the systemic risk? Unfortunately, this is very difficult, and we are not very good at it, e.g. the order of magnitude of the probability of failure of a nuclear plant is still ungraspable. It seems that this is because most of the familiar correlation structures in probability are low-dimensional, or even onedimensional. However, correlation structures in complex systems are high-dimensional and usual independence assumption is seriously violated. The goal of this research project is to find efficient algorithms for systemic risk measurement by defining a new class of models of highdimensional correlation structures in a large collection of random variables. The defined models should be computationally tractable and simple enough so that one can bring them to data and use it for various applications in high-dimensional data analysis. In this project we will continue to use the methods of mathematical and computational modeling, specifically: complex networks, sparse estimation, and concentration of measure. With this approach, we have already obtained very important results, like an insight into the emergence of power-law and two-phase behavior in the financial market fluctuations. Also, with this approach we would like to better understand the basic mechanisms that underlie systemic risk and the stability of the complex systems, e.g. financial system. The need for scientific foundations for a systemic risk measure is more than an academic concern as different people around the world consider how to reduce the risks and costs of systemic crises. The goal of this research project is to find efficient algorithms for systemic risk measurement by defining a new class of models of high-dimensional correlation structures in a large collection of random variables. The objectives of this research project in the equal order of priority: 1. Define new class of models of high-dimensional correlation structures in a large collection of random variables using dynamic complex networks (i) Develop new cluster-chained network models that can generate multivariate time series with predefined statistical properties (ii) Perform a theoretical analysis of the network models using concentration of measure methods and exploiting other blessings of dimensionality 2. Develop method for sparse estimation of dynamic network structure from multivariate time series 3. Develop efficient algorithms and tools for systemic risk measurement using the defined network models and the sparse estimation method