This paper studies stabilities of stochastic differential equation (SDE) driven by timechanged Lévy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics, biology, engineering, finance and hydrology. Necessary conditions for solution of time-changed SDE to be stable in different senses will be established. Connection between stability of solution to time-changed SDE and that to corresponding original SDE will be disclosed. Examples related to different stabilities will be given. We study SDEs with time-changed Lévy noise, where the time-change processes are inverse of general Lévy subordinators. These results are important improvements of the results in Wu [17].

This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian Lévy processes, with space-time-dependent drift, diffusion and jump coefficients, thus significantly extends Magdziarz and Zorawik's result in [14]. Fractional Fokker-Planck equation describing subdiffusion is solved by our result in full generality from perspective of stochastic representation.A stochastic process X = {X(t), t ≥ 0} is a Lévy process if (a) X(0) = 0, a.s., (b) X has independent and stationary increments, (c) X is stochastically continuous in time. X − (t) is used to denote left limit, X − (t) = lim s→t− X(s).

This paper studies path stabilities of the solution to stochastic differential equations (SDE) driven by time-changed Lévy noise. The conditions for the solution of time-changed SDE to be path stable and exponentially path stable are given. Moreover, we reveal the important role of the time drift in determining the path stability properties of the solution. Related examples are provided.

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Purpose This paper aims to construct a measure of integration among global banks and examine its impact on bank insolvencies and bank crises. Design/methodology/approach The authors apply principal component analysis to measure a bank’s degree of integration to the global banking market. Moreover, they test whether bank integration affects bank insolvency risk, in which they treat the equity of individual banks as a call option. Findings The authors find that the banking industry has become more globally integrated over the past two decades. At the individual bank level, results indicate that banks with higher integration levels have more assets, more nontraditional banking services and more interbank businesses. Overall, they find that a bank’s integration level is negatively associated with insolvency risk, which suggests that greater integration with global markets diversifies a bank’s risk. At the country level, banking systems with less integrated big banks, or more integrated smaller banks, are more stable and hence less likely to suffer a banking crisis. Originality/value The authors construct a novel measure of integration among global banks and examine its impact on bank insolvencies and bank crises.