Quantitative analysis of systemic risk: from traditional collective risk assessment to resilience concept

We live in a complex world: today’s societies are interconnected in complex and dynamic socio-technological networks and have become more dependent on the services provided by critical facilities. In coming years, climate change is expected to exacerbate these trends. In this context, systemic risk assessment is a worldwide challenge that institutions and private individuals must face at both global and local scales. The aim of this work is to adapt the traditional risk assessment methodology to the concept of resilience in order to quantify disaster resilience of a complex system by means of the graph (i.e., the mathematical representation of the system element and connections). We showed that is necessary to adapt the traditional risk assessment to resilience concept considering that the consolidaded definition, provided by the United Nations General Assembly in 2017, includes two fundamental features of systemic risk: (1) resilience is a property of a system and not of single entities and (2) resilience is a property of the system dynamic response.

The methodology proposed represents the elements of the system and their connections (i.e., the services they exchange) with a weighted and redundant graph exposed to extreme weather events and societal systems: river and pluvial floods in urban area. The quantitative analysis of systemic risk is characterized by three activities: 1) assess the systemic properties in order to highlight the centrality of some elements; 2) show how each element can dynamically adapt to an external perturbation, taking advantage of the redundancy of the connections and the capacity of each element to supply lost services; 3) quantify the resilience as the actual reduction of the impacts of events at different return periods.

To illustrate step by step the proposed methodology and show its practical feasibility, we applied it to a pilot study: the city of Monza, a densely populated urban environment.