Michael Perelman wrote:
For anybody interested in the theory of mathematical finance theory, I would suggest: MacKenzie, Donald A. 2006. An Engine, Not a Camera (Cambridge: MIT Press). Not only does he go through the mechanics, but he interviews the central figures in its development.
I truly recommend Salih Neftci's _Introduction to the Mathematics of Financial Derivatives_. He gives an informal, yet transparent, intuitive derivation of the arbitrage theorem (the "fundamental theory of finance") and Ito's lemma. These are two workhorses of finance theory. The former helps to calculate the risk-neutral synthetic probabilities that underlie exact option pricing and the latter is the notion of stochastic "integration," which you need to solve stochastic differential equations. If you don't have a strong background on measure theory (the superset of probability theory) and stochastic calculus, he's da man. And that's the case with most people approaching finance theory from the social science side -- as opposed to the physics side. It is not rocket science... hmm, well, it kind of is -- but it's too powerful to be left only to the physicists and mathematicians.
