
Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don't realize is that he has also been watching patterns of market change. In The (Mis)Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like. The result is a revolutionary reevaluation of the standard tools and models of modern financial theory. Markets, we learn, are far riskier than we have wanted to believe. From the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate--Mandelbrot shows that the world of finance can be understood in more accurate, and volatile, terms than the tired theories of yesteryear.The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With The (Mis)Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401(k) holders. Markets will never be seen as "safe bets" again.
For Mandelbrot, I'd recommend starting with The (Mis)Behavior of Markets. For Taleb, maybe start with The Black Swan.
With those books you'll be able to fully understand why even if/when AI becomes sentient, it will still not help avoid blow ups.
(One reason among many others is, for example, that there are things that cannot be properly forecasted, no matter how hard you try or how advanced your model is, doesn't matter, there's a limit to what we can know and what we can't know about the future...)
Extra: Check out also Thorp's A Man for All Markets.
Many here have mentioned "A Random Walk Down Wall Street"; let me add that there exists a book called "A Non-Random Walk Down Wall Street", but I haven't read it yet.
Browse Wikipedia on any trading-related topic you find interesting and you are probably going to find some books, such as "The Quants" https://en.wikipedia.org/wiki/The_Quants
Finally, you might want to check out the works of Jack Schwager [1], Michael Lewis [2] or Ed Thorpe [3].
[1] https://en.wikipedia.org/wiki/Jack_D._Schwager
The Emperors New Mind - Roger Penrose
Godel, Escher, Bach - Douglass Hoffstadter
Brocas Brain - Carl Sagan
The (mis)Behavior of Markets - Benoit Mandelbrot
The Black Swan - Nicholas Nassem Taleb
Fiction
Gates Of Fire - Stephen Pressfield
Neuromancer - William Gibson
Snow Crash - Neal Stephenson
Hardwired - Walter Jon Williams
Altered Carbon - Richard Morgan
Red Mars - Kim Stanley Robinson
Space - Stephen Baxter
Enders Game - Orson Scott Card
Skeleton Crew - Stephen King
I've given away a lot of books. I'm old.
A great read on an alternative view on the topic of using statistics for finance is The (Mis)Behavior of Markets by Benoit Mandlebrot [1]. It's very well written, basic enough for most to comprehend and first book on finance I read in college (before I went on to major in finance + math).
The aforementioned book has some very interesting notions with Trading Time being my favorite. Basically one can near-perfectly "forge" financial data with fractal objects called "financial cartoons" [2]. The objects are composed to two distinct fractals - one for price vs trading time and another for trading time vs clock time [3]. The latter rescales the volatility seen former, either compressing or expanding it. Rescaling volatility isn't a new idea, but it was a parallel "discovery".
There has been some work on figuring out how to use Fractal Geometry to analyze financial time series data but it's still in its infancy. The problem is figuring out how to transform the data into the fractals domain + figuring out what the results from a fractal based analysis would mean for forecasting future events. I've been working on these problems for many years (in earnest in college and as a hobby thereafter) but made little true progress.
[1] http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...
[2] http://classes.yale.edu/fractals/randfrac/Market/Fake/Fake.h...
[3] http://classes.yale.edu/fractals/randfrac/Market/TradingTime...
You may enjoy this book if you are interested in Financial Markets, have some knowledge of Efficient Market Theory, and aware of existence of Fractal Geometry.
http://www.amazon.com/The-Misbehavior-Markets-Financial-Turb...