RWRI Part 4: Let’s Get Extreme

This article is the fourth of a 5-part series covering the Real World Risk Institute’s 1-week mini-course on Real World Risk, held in NYC. There’s statistics, complex systems theory, and strong opinions ahead. I’ve learned far more than I can adequately represent here, so these will more or less be my raw notes. You can find Part 1 and a Table of Contents here.

Complexity is synonymous with unintended consequences

The following notes are based on a guest lecture by Andrea Fontanari. I’ll try not to butcher his message.

Extreme Value Theory (EVT)

Statistics = data + assumptions.

The point of EVT is to try to uncover the behavior of the tail of the distributions. Things tend to be interesting in the tails, as we’ve established by now.

The first part of studying the tail is answering a simple question: where does the tail start? The short answer is that you have to guess. Generally, tail behavior of most distributions is driven by a couple heuristics

The extreme value index ( γ= 1/α)

Fréchet domain (if γ>0 and α>0, the tail is heavy)

• Pareto distributions, α stable distributions…