My introduction to finance came back in graduate school when a friend working at an option shop in NY asked me to explain Edgar Peters’s Fractal Market Analysis to him. This is probably a pretty non-standard first introduction to finance, but it was a lucky one for me – I found the presentation to be compelling. Two other books that helped me refine my thinking on finance were both by Mandelbrot – The (Mis) Behavior of Markets and Fractals and Scaling in Finance.
My only bit of background in finance that would be considered “standard” by the business school crowd came from reading Zvi Bodie’s paper “On the Risk of Stocks in the Long Run”. This paper asks a simple, but quite educationally useful, question about option pricing via Black-Scholes – what is the price a European put maturing in the future with a strike price equal to the current price of the asset brought forward to the maturity date at the risk free rate? The answer was a surprise to me (though, of course, I’d not studied much option pricing, so anything would have been a surprise, I suppose) and understanding that result proved to be useful many years later when the friendly Wall St. folks showed up wanting to write 15 and 20 year puts with us.
With that all as background, this ~30 minute talk by Nassim Taleb has the most important piece of math that I learned in 2015:
These screen shots in particular show two parts that have stuck with me since the moment I saw them. The first shows roughly how much data you need to be able to talk sensibly about something governed by a power law distributions, and the second makes the point that if you try to estimate the mean of a power law distribution ( with 1 < 
If you are analyzing anything that lives in (to borrow Taleb’s word) extremistan, you have to understand the ideas in Taleb’s talk. If you don’t, the slides I highlighted show two easy traps that you’ll fall into – and there many are others, too.
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