From its historical roots to the present, insurance can be described as "the taming of uncertainty." From a more mathematical point of view, Jakob Bernoulli's 1713 Law of Large Numbers explains how averages of similar but independent risks are well approximated by the mean loss size (the fair premium) of one such risk. Without doubt, this result can be referred to as The Fundamental Theorem of Insurance. At its basis however lies the notion of randomness, a precondition without which insurance would not be possible; insurance aims at hedging away the uncertainty underlying an insurable risk.

And yet, almost a century after Kolmogorov's classic on The Foundations of Probability Theory (1933), we still struggle with the basics: "What is a random event?" In the wake of recent political and financial crises, Known Unknowns and Black Swans trouble our minds. Frank Knight's Risk, Uncertainty and Profit (1921) and John Maynard Keynes' General Theory (1936) have become essential reading again for all students in economics and finance. These authors discussed, or better, questioned, the differences between the notions of risk and uncertainty. And whereas we as actuaries could hide behind: "We always knew about the differences between epistemic, ontological and aleatoric risk," it is much less clear how to use this "We always knew..." in practice.

Where does all this leave the practicing actuary faced with the pricing of longevity risk, annuities, and catastrophic environmental risks; the actuary who is involved in discussions about sense and sensibility of new regulatory guidelines around Solvency 2?

In this talk, Dr. Embrechts will discuss some of these background issues, and concentrate specifically on some aspects of quantitative risk management related to the modeling of extremes, and on the model and parameter risk underlying current issues occupying the world of insurance.