I recently experienced my own “deflate-gate” (today is Super Bowl Sunday). I’ve always enjoyed mathematics and was a math major in college. So I confess, I have an (over?) inflated sense of my math skills. I was shocked to learn there was a whole different kind of calculus that I never knew even existed — stochastic calculus.
So I’ve been reading Steven Shreve’s books on Stochastic Calculus for Finance, volumes 1 and 2. This topic is certainly not for everyone, but if the topic interests you at all, this is a great introduction. I tried reading An Introduction to the Mathematics of Financial Derivatives three years ago, but it was just too dense and too poorly described to be of any real use, and I gave up. Recently, I decided to try again—this time with Shreve’s book. It is the contrast between these two books that really makes me appreciate the wonderful job Shreve has done explaining this topic.
I’m interested in financial topics generally because of my job of applying IBM’s Watson technology to the financial domain. Not that there was a pressing need for stochastic calculus in my job, but hey, you never know how a piece of knowledge might be useful until you need it.
One example of an interesting, yet unforeseen connection, is the possibility of applying some of the financial ideas and concepts to multiagent systems. A financial option between a buyer and a seller is similar to a conditional commitment between a debtor and a creditor. The seller/debtor is limiting his future actions. This represents a cost to the seller/debtor and a benefit to the buyer/creditor. The question I’ve been recently pondering is: can I adapt the financial concepts for pricing a financial option to commitments?
As an aside, even thought Shreve covers many substantial mathematical topics, one of the best things about his books is his writing style. The prose is amazingly light for a mathematical text. He frequently puts the material back into context by drawing connections between topics. This does a LOT to help the reader see where we’ve been, where we currently are, and where we’re headed. In addition to dissecting the math, I’ve also dissected some of his prose. There are many elements of his prose I’d like to incorporate into my own writing style.