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With the increasing trend of global population aging, traditional risk assessment methods often overlook the nonlinear interactions and dynamic feedback mechanisms between various elements in the system, making it difficult to capture the complex process of risk evolution. This study identified and characterized the complex relationships between participants in the pension financial system through complex network analysis, including fund flows, policy impacts, market fluctuations, and other dimensions. Then, partial differential equations (PDEs) were introduced as the core modeling tool, and a pension financial system based on partial differential equations (PFS-PDE) risk dynamic evolution model was established by combining PDEs. The PFS-PDE model achieved a relatively high intersection over union (IOU) value after fewer training iterations (about 30) and remained relatively stable thereafter, indicating that the model has a fast convergence speed. The PFS-PDE model has relatively low mean square error (MSE) values and a relatively small fluctuation range under most training iterations, which can be considered as a relatively better performance. Compared with other models, the PFS-PDE model has a smaller range of MSE value fluctuations, indicating that the model has high stability during the training process.

This paper studies the autonomous uncertain and stochastic systems with multiple delays, which describe a financial system involving the interest rate, the investment demand and the price index. For the deterministic model associated to the uncertain financial system, we set the conditions for the existence of the delay parameter value for which the model displays a Hopf bifurcation. For the stochastic system, we identify the differential equations for the mean value as well as for the square mean value. The last part of the paper includes numerical simulations and conclusions.

The dynamic behavior of a new financial system with diffusion effect and two delays is studied. The local stability of equilibrium is studied by analyzing the corresponding characteristic equation and developing the crossing curve method. Hopf bifurcation curves are obtained by three procedures and the critical value of delay of Hopf bifurcation is obtained. By using the central manifold theorem and the normal form theory of partial differential equations, the normal form of Hopf bifurcation with two delays is derived, and the bifurcation direction and the stability of periodic solution are determined. The numerical simulations not only verify these theoretical results, but also show that double Hopf bifurcation may occur and the two delays play a key role in chaos suppression. This study has important theoretical value of innovation and practical value in the macro-economic system.

The emergent global economy depends on financial growth. Social and economic development is achieved by a stable, growing, and secure financial chain system. Financial instability poses huge financial inflation and economic decline. The financial crisis and the turbulence of the finance market also result in deterministic instability. This fluctuation during the financial operation may also critically affect the development of the economic system and other sociological and financial stabilities. For the chaotic behavior of the finance system, the mathematical formulation is developed along with controlling terms in this paper. Fitting the controlling parameters, the financial model can be made secure and safe from periodic behavior and will run in chaotic conditions. At the first attempt, the dynamical system and the controlling parameters are adjusted through assigned values and their ranges. Second, the impact of these parameters is studied along with the feasible techniques by graphical representations. The said financial dynamics are investigated in the sense of fractal–fractional derivatives. The concept of Ulam–Hyers stability is also developed for the considered model.

This paper examines big data analytics implications on the central banking financial system’s technological progress. A digital technological progress framework and model is established to analyze the economy’s aggregate supply via covering the monetary policy, big data analytics, pollutants emissions as independent variables and the economy’s aggregate demand as a moderating variable in a modified extensive growth theory framework and model to compute the productivity indicators and the total factor productivity (TFP) as the central banking technological progress that combined the mentioned variables qualities contribution. Besides, data analytics positive and negative externalities that include data analytics shortcomings as unpriced undesirable output in the form of cybersecurity and pollutants’ emissions among other proxies are internalized in the framework and the model to integrate the digital technology innovation with digital technology shortcomings and climate change. This revised extensive theory framework and model is a remarkable technique comprehensive of the technological progress matters and sustainable economic development and is considered one of the most important sustainable development and long-run economic growth proportions in the central banking financial system functions to manage the economy’s aggregate supply and demand that unnoticed by previous studies.

This paper explores how the overall development of the financial sector and the regulatory framework impact national levels of microfinance outreach. It finds that microfinance tends to serve more clients in less developed, less competitive financial systems. However, it also finds that the microfinance sector is able to reach more clients where government policy is conducive to business development. These seemingly contradictory findings have important implications for the future of microfinance. On the one hand, the success of microfinance can be strengthened by broader business-oriented reforms. On the other hand, it may lose relevance as the formal financial sector develops and reaches more of the population.

In this paper, by using the "clearing payment concept" initially introduced by Eisenberg and Noe (2001, Systemic Risk in Financial Systems. Management Science, 47(2), 236–249), under general framework of financial system (network) in an interbank network, we first discuss the mechanics of systemic risk's contagions related to assets' recovery rate, and capital requirement. Then under the general regularity condition for the financial network, we discuss some new results for the existence, uniqueness, and continuity results which could be regarded as the fundamental supporting for the systemic risk measurement in terms of numerical analysis with simulations in the practice.

The article explores the effects of financial depth and market structure on banking stability for 24 advanced economies and 18 emerging economies over the period of 2003–2010. We examine how commonality in banking stability varies from emerging markets to advanced nations. Our findings suggest possible explanations for what affects the banking stability with economic transitions on the dynamics evolving from emerging to advanced economies.

This work aims to understand current trends in the financial sector. Many trends are the technological solutions provided by new players operating in the financial sector (fintech), leading to different perspectives for the future awaiting private citizens and companies. This work presupposes the need to understand how the traditional financial system is able to keep up with the continuous and changing demands of a society that is evolving towards 4.0 and is increasingly aiming to meet environmental, social, and governance sustainability criteria. Above all, this chapter requires an understanding of the real reasons why systems such as decentralised finance are taking over despite the presence of well-established players. In this work, the authors aim to investigate the players, the battleground of a clash between tradition and innovation in the financial field, and whether the measures adopted by the banking system to adapt to the trends of technological innovation are sufficient to stand up to a real model of innovative development which sees a closer relationship between stakeholders and companies and which is far from the traditional banking–company system.

The financial crisis, the accumulation of sovereign debt, shocks to commodity prices, and pandemics are just a few of the recent economic crises that have affected the world and had a major effect on economic activities. In this context, the financial sector must fully contribute to encouraging economic growth in order to achieve equitable economic growth and reduce poverty. To that end, access to affordable and secure financial services is crucial. The main goal of financial inclusion, which allows people to take advantage of saving and investing opportunities, is to provide basic financial services to society’s poor and excluded groups. This study aims to identify the factors that promote financial inclusion in the MENA region. It specifically examines the impact of GDP per capita, the money supply as a percentage of GDP, the number of internet users as a percentage of the population, and consumer price inflation. The International Monetary Fund and the Global Development Indicators provided the secondary data for the study, which covers the period 2004–2020. The dynamic panel was conducted using Stata 17 software to obtain the coefficients of such variables that affect the levels of financial inclusion in six MENA countries. The results reveal that income level, measured by GDP per capita, financial sector development, measured by the money supply, and the number of internet users all have positive effects on financial inclusion in the MENA region, while consumer price inflation has no impact. The Financial Inclusion Index (FII), according to Sarma’s (2008) approach, has not been employed in any relevant studies, despite the theoretical and empirical literature offering a range of perspectives on which factor can determine financial inclusion. This study uses this index to measure financial inclusion and then applies dynamic panel estimation to identify the factors that promote financial inclusion in MENA countries. Consequently, this chapter strives to enrich the literature by comprehending the determinants of financial inclusion in the MENA region, covering the period 2004–2020.