Risk spillover networks in financial system based on information theory

Since the financial system has illustrated an increasingly prominent characteristic of inextricable connections, information theory is gradually utilized to study the financial system. By collecting the daily data of industry index (2005-2020) and region index (2012-2020) listed in China as samples, this paper applies an innovative measure named partial mutual information on mixed embedding to generate directed networks. Based on the analysis of nonlinear relationships among sectors, this paper realizes the accurate construction of “time-varying” financial network from the perspective of risk spillover. The results are presented as follow: (1) interactions can be better understood through the nonlinear networks among distinct sectors, and sectors in the networks could be classified into different types according to their topological properties connected to risk spillover; (2) in the rising stage, information is transmitted rapidly in the network, so the risk is fast diffused and absorbed; (3) in the declining stage, the network topology is more complex and panic sentiments have long term impact leading to more connections; (4) The US market, Japan market and Hongkong market have significant affect on China’s market. The results suggest that this nonlinear measure is an effective approach to develop financial networks and explore the mechanism of risk spillover.

Nonlinear Measure for Nonlinear Dynamic Processes Using Convergence Area: Typical Case Studies

Several industrial chemical processes exhibit severe nonlinearity. This paper addresses the computational and nonlinear issues occurring in many typical industrial problems in aspects of its stability, strength of nonlinearity and input output dynamics. In this article, initially, a prospective investigation is conducted on various nonlinear processes through phase portrait analysis to understand their stability status at different initial conditions about the vicinity of the operating point of the process. To estimate the degree of nonlinearity, for input perturbations from its nominal value, a novel nonlinear measure is put forward, that anticipates on the converging area between the nonlinear and their linearized responses. The nonlinearity strength is fixed between 0 and 1 to classify processes to be mild, medium or highly nonlinear. The most suitable operating point, for which the system remains asymptotically stable is clearly identified from the phase portrait. The metric can be contemplated as a promising tool to measure the nonlinearity of Industrial case studies at different linear approximations. Numerical simulations are executed in Matlab to compute , which conveys that the nonlinear dynamics of each Industrial example is very sensitive to input perturbations at different linear approximations. In addition to the identified metric, nonlinear lemmas are framed to select appropriate control schemes for the processes based on its numerical value of nonlinearity..