Risk analysis is a sophisticated technology developed over the past 250 years to estimate the potential for financial loss in games of chance. In modern times, the technology has been applied to a wide variety of disciplines in engineering, social and political science, and, of course, the stock market. At the heart of risk analysis is a simple idea—risk is expected gain or loss under uncertainty. Daniel Bernoulli established the expected utility theory (EUT) as the earliest known method of quantifying risk in terms of likelihood and gain/loss—R = Pr(c)C, where C is consequence in terms of gain or loss and Pr(c) is the probability of a gain or loss equal to C. Modern risk analysis is descended from Bernoulli's earliest work on EUT. In the field of critical infrastructure protection (CIP), probabilistic risk analysis (PRA) was the earliest application of EUT used to assess risk in infrastructure systems. More recently, Bernoulli's EUT has been blended together with Bayesian belief networks, game theory, and probable maximum loss (PML) theory to arrive at today's foundation of risk assessment in homeland security.
The reader in need of a probability primer is advised to review Appendix A, and the advanced reader wanting to understand the mathematical details underlying the survey given here is advised to read Appendix B. The following concepts and results are covered in this chapter: