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Nowadays, increase of the analyzing stock markets as complex systems lead graph theory to play key role. For instance detecting graph communities is an important task in the analysis of stocks, and minimum spanning trees let us to get important information for the topology of the market. In this paper, we introduce a method to build a connected graph representation of Borsa Istanbul based on the spectrum. We, then, detect graph communities and internal hierarchies by using the minimum spanning trees. The results suggest that the approach is demonstrably eective for Borsa Istanbul sessionally data returns.

Getting access to sufficient funding is the keystone for the development of any business, but especially for small and medium enterprises (SMEs). These economic entities are crucial players in the global economy since they include almost 90% of companies, provide jobs for nearly 50% of the global workforce, and enhance long-term economic growth. In this context, our study explores important sources concerning the financing of small and medium enterprises and their impact on economic growth during the period 2005–2020 with data from SMEs covering the 28 countries belonging to the European Union. The set of predictors included Strength of legal rights index, Days sales outstanding, Bad debt loss, Interest rate, Bank support, Business angels, Private lenders, and Public support. The set of dependent variables included Cost of loans, Equity fund, GDP growth rate, and Value added growth rate. Our methodological approach was complex, it considered a panel data analysis with a first-difference generalized method of moments estimator and a multiplex time series analysis. The novelty of the study resides in combining the two methods in order to investigate significant drivers of economic growth across the EU. Empirical results showed that economic growth was mainly triggered by predictors such as Interest rate, Business angels, Bank support, and Public support. Moreover, the valuable mathematical insights elicited by the multiplex time series analysis suggested that European economies cooperated intensively through SME activities. Based on our empirical results, national and regional authorities should enact adequate policies to support business endeavors of small and medium enterprises.

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Abstract:In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

In this study, we present a model which represents the interaction of financial companies in their network. Since the long time series have a global memory effect, we present our model in the terms of fractional integro-differential equations. This model characterize the behavior of the complex network where vertices are the financial companies operating in XU100 and edges are formed by distance based on Pearson correlation coefficient. This behavior can be seen as the financial interactions of the agents. Hence, we first cluster the complex network in the terms of high modularity of the edges. Then, we give a system of fractional integro-differential equation model with two parameters. First parameter defines the strength of the connection of agents to their cluster. Hence, to estimate this parameter we use vibrational potential of each agent in their cluster. The second parameter in our model defines how much agents in a cluster affect each other. Therefore, we use the disparity measure of PMFGs of each cluster to estimate second parameter. To solve model numerically we use an efficient algorithmic decomposition method and concluded that those solutions are consistent with real world data. The model and the solutions we present with fractional derivative show that the real data of Borsa Istanbul Stock Exchange Market always seek for an equilibrium state.

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Stock market networks commonly involve uncertainty, and the theory of soft sets emerges as a powerful tool to handle it. In this study, we present a soft analogue of the differential of a vibrational potential function acting on a stock market network as vibrational force. For this purpose, we first study the vibrational potential function operating on each vertex by using the Laplacian of the neighborhood graph, then applied the soft approximator for the soft sets where the data points are embedded to Euclidean n space. We used the data of the globally operating leading stock markets of 17 countries and presented the results respect to them.