This chapter provides the tools to compute catastrophe (CAT) risk, which represents a compound measure of the likelihood and magnitude of adverse consequences affecting structures, individuals, and valuable assets. The process consists of first establishing an inventory of assets (here real or simulated) exposed to potential hazards (exposure module). Estimating the expected damage resulting from a given hazard load (according to Chapter 2) is the second crucial step in the assessment process (vulnerability module). The application of damage functions to exposure data forms the basis for calculating loss estimates (loss module). To ensure consistency across perils, the mean damage ratio is used as the main measure for damage footprints D(x,y), with the final loss footprints simply expressed as L(x,y) = D(x,y) × ν(x,y), where ν(x,y) represents the exposure footprint. Damage functions are provided for various hazard loads: blasts (explosions and asteroid impacts), earthquakes, floods, hail, landslides, volcanic eruptions, and wind.

This chapter goes beyond the description of individual events by covering extremes caused by a combination of multiple events. Two main types of interactions are covered: domino effects and compound events. Domino effects, which represent one-way chains of events, are quantified using Markov theory and graph theory. Compound events, which include complex feedback loops in the complex Earth system, are modelled with system dynamics (as in Chapter 4). Two such systems are provided, the ESCIMO climate model and the World2 model of world dynamics. The impact of global warming, pollution, and resource depletion on catastrophes is investigated, as far as ecosystem and societal collapse. The types of catastrophes considered in this chapter are as follows: storm clustering, earthquake clustering (with accelerated fatigue of structures), domino effects at refineries (explosions, fires, toxic spills), cascading failures in physical networks (more precisely blackouts in a power grid), rainforest dieback, lake eutrophication, and hypothetical human population collapse.

This final chapter demonstrates how the catastrophe (CAT) models described in previous chapters can be used as inputs for CAT risk management. CAT model outputs, which can translate into actionable strategies, are risk metrics such as the average annual loss, exceedance probability curves, and values at risk (as defined in Chapter 3). Practical applications include risk transfer via insurance and CAT bonds, as well as risk reduction, consisting of reducing exposure, hazard, or vulnerability. The forecasting of perils (such as tropical cyclones and earthquakes) is explored, as well as strategies of decision-making under uncertainty. The overarching concept of risk governance, which includes risk assessment, management, and communication between various stakeholders, is illustrated with the case study of seismic risk at geothermal plants. This scenario exemplifies how CAT modelling is central in the trade-off between energy security and public safety and how large uncertainties impact risk perceptions and decisions.

This introductory chapter, encyclopaedic in nature, covers the main aspects of catastrophe (CAT) risk from a qualitative perspective, offering an overview of what will be explored in quantitative terms in the subsequent chapters. It starts with the definition of the fundamental terms and concepts, such as peril, hazard, risk, uncertainty, probability, and CAT model. It then describes the historical development of catastrophe risk science, which was often influenced by the societal impact of some infamous catastrophes. The main periods are as follows: from ancient myths to medieval texts, mathematization (eighteenth and nineteenth centuries) and computerization (twentieth century). Finally, it provides an exhaustive list of perils categorized by their physical origin, including geophysical, hydrological, meteorological, climatological, biological, extraterrestrial, technological, and socio-economic perils. In total, 42 perils are covered, with historical examples and consequences for people and structures discussed for each one of them.

This chapter describes three main numerical methods to model hazards which cannot be simplified by analytical expressions (as covered in Chapter 2): cellular automata, agent-based models (ABMs), and system dynamics. Both cellular automata and ABMs are algorithmic approaches while system dynamics is a case of numerical integration. Energy dissipation during the hazard process is a dynamic process, that is, a process that evolves over time. Reanalysing all perils from a dynamic perspective is not always justified, since a static footprint (as defined in Chapter 2) often offers a reasonable approximation for the purpose of damage assessment. However, for some specific perils, the dynamics of the process must be considered for their proper characterization. A variety of dynamic models is presented here, for armed conflicts, blackouts, epidemics, floods, landslides, pest infestations, social unrest, stampedes, and wildfires. Their implementation in the standard catastrophe (CAT) model pipeline is also discussed.