“In this chapter, we present some key results from extreme value theory (EVT) and illustrate how EVT can be used to supplement traditional statistical analysis. We use EVT when we are concerned about the impact of very rare, very large losses. Because they are rare, we are unlikely to have much data, but using EVT we can infer the extreme tail behaviour of most distributions.

There are two different, but related types of models for extreme value analysis. The first considers the distribution of the maximum value in a random sample of losses. These are called the block maxima models. The second comes from analysing the rare, very large losses, defined as the losses exceeding some high threshold. These are the points over threshold models.

We present the key results for both of these, and show how they are connected. We derive formulas for the VaR and Expected Shortfall risk measures using EVT that are useful when the loss distribution is fat-tailed, and the parameter a is close to 1.0. We use examples throughout to highlight the potential uses in practical applications.”

An economic scenario generator (ESG) is a joint model of economic indicators that is designed for use in risk measurement and risk management. Using Monte Carlo simulation, the ESG generates random paths for variables such as interest rates, inflation rates, and stock index movements, designed to reflect both suitable marginal distributions for each variable, and the dependencies between variables. In this chapter, we consider first the decisions that need to be made before the model is constructed or selected. We then present two different frameworks used for ESGs: the cascade design and the vector autoregression design. We consider some of the challenges of model and parameter selection for long-term forecasting, such as structural breaks in the historical data. Finally, we illustrate the application of ESGs with an example involving an employer-sponsored pension plan.

“In this chapter, we consider how traditional measures of profit, using return ratios, can be improved by considering the riskiness of the investment. The objective is to analyse which parts of the business are performing best relative to the risks involved, rather than simply comparing returns with no consideration of risk. In turn, this allows the business to decide where it should take on more risk, as the additional risk is justified by additional return, and where it should take on less.

A key part of the risk budgeting exercise is the allocation of the organization’s economic capital to the individual business units. In the second part of this chapter, we describe different approaches to capital allocation, and assess their relative advantages and disadvantages.”

In this chapter, we discuss how to prepare for and respond to crises. Crises are inevitable, and preparing for crises is an important aspect of risk management. Effective preparation requires the firm to understand best practice in crisis response. We present some examples, good and bad, of corporate and government responses to crises. We discuss the key steps in crisis preparation, followed by the key steps in crisis response. Finally, we consider the impact of corporate structure and ethics.

This chapter describes software construction and testing. These are the very concrete steps in the software life cycle (Section 14.1). Next, we discuss “construction,” or coding (Section 14.2), beginning with a brief review of key regulatory issues. We follow this with a presentation of programming topics and conclude this section with an extended discussion of risk management in the context of the programming process.

This chapter presents an overview of current medical software applications and the factors that promise to drive growth in this area. We begin this chapter by defining and discussing some important terms such as digital biomarkers and digital health (Section 7.1).

We can distinguish at least three different ‘ways of thinking’ about democracy in the EU. In the first camp we find the statists, who argue that the EU exercises real power in highly salient policy domains and should be held to the same democratic standards as the nation state. The second camp is composed by those arguing that the EU should be thought of as a demoicracy. This is a variation on the statist account of democracy, seeing the EU as an institution that consists of Member States with common objectives but separate interests. Its institutional configuration should reflect this. The third camp is one that centres on consociational democracy. This model focuses on forging consensus between different interest groups in society rather than seeking to structure politics (at whichever level) to forge majoritarian rule. As we will see in this chapter, the question whether the EU is, or can be, a true political union, can be answered (equally convincingly) in many different ways.

It is an understatement to say that law is important in the process of European integration. Understanding the EU without understanding the particular (and peculiar) role that law has assumed in the first decades of European integration is impossible. By making it legally impossible for Member States to resist the application of both specific norms of EU law and the general objectives of European integration, EU law gets European integration ‘done’. The CJEU’s understanding of the EU legal order as something that is hierarchically superior and autonomous from national legal systems, however, irritates national legal systems, which are increasingly articulating limits to the process of ‘integration through law’. This tension has become more pronounced as the EU moves into policy domains that are politically more salient and touch on Member States’ core powersThis indicates a fragility at the core of an EU that is, fundamentally, a legal order.

This chapter provides background on the constraints imposed on software by the need to operate within a healthcare environment. We first present an overview of the environment and the constraints under which our software must operate (Section 3.1).

This chapter describes the process of software validation. We first begin with a brief overview of what validation is. We then review the regulatory guidance for validation (Section 15.1) in general, and then provide an extended discussion on the issues that affect the validation of software modules that use artificial intelligence/machine learning (AI/ML) techniques in particular.