On a new stochastic model for cascading failures

Abstract

In this paper, to model cascading failures, a new stochastic failure model is proposed. In a system subject to cascading failures, after each failure of the component, the remaining component suffers from increased load or stress. This results in shortened residual lifetimes of the remaining components. In this paper, to model this effect, the concept of the usual stochastic order is employed along with the accelerated life test model, and a new general class of stochastic failure models is generated.

A Stochastic Model for Cascading Failures in Financial Networks

“…For both noise parameters we can observe an inverse relation between the probability of failure and the primitive assets' values, since the nodes with higher primitive assets' values have lower probability of failure. In the same way as in the two previous simulations, this behavior seems to be in accordance with (15) in Theorem 1. It is also important to observe that when we increase the noise parameter, and set K = 300, the probability of failure increases over time for all the companies in the network.…”

“…Note that, for both noise parameters the nodes with higher degree, which correspond to the companies with higher number of cross-holdings, are more vulnerable and they have higher probabilities of failure. Intuitively, one can say that this behavior is in accordance with (15) in Theorem 1. Furthermore, it is also important to observe that when we increase the noise parameter, K = 300, we have faster dynamics since higher probabilities of failure propagate faster among the nodes.…”

“…The entanglement of financial and biological interdependent contagion networks is analyzed in [13]. Stochastic models to determine the moment of the first failure in a financial network are developed in [14] and [15]. The stochastic model of a diversified cross-shareholding network is studied in [16].…”

“…For each company, we simulate the sample error according to dynamics (12), the mean error according to dynamics (15) and the variance error according to dynamics (22). The results are depicted in Fig.…”

A model for stochastic dependence implied by failures among deteriorating components

“…To be more specific, we here assume that a failure among components has an impact on the future deterioration of the surviving components and we call it stochastic failure dependence. This kind of dependence has been envisioned in different papers such as References 13‐16, where the authors model the impact of failures on the lifetimes of the surviving components (including possible cascading failures), see also Reference 12 for many other models and references. However, the papers involving Lévy deteriorating components together with stochastic failure dependence are fewer.…”