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I'm currently taking this Coursera course on financial engineering, which is fine but it's very focused on applications instead of proofs. They recommend Investment Science as a companion text, but some of the comments on Amazon seemed to indicate that this book also isn't very proof oriented. I've also heard of Options, Futures and Other Derivatives as a recommended text, but again the Amazon comments indicate that this might not be very rigorous.

Are there any texts which require a similar amount of knowledge about finance but are more math focused? If it's relevant, my background is in pure math so I'm decently skilled mathematically but I may have forgotten some particulars about calculus and probability.

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  • $\begingroup$ OFOD has proofs in its appendices... $\endgroup$
    – BCLC
    Commented Dec 25, 2014 at 13:25

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The first book that comes to mind that is written in the style of Definition - Proposition - Proof is:

  1. Bjork - Arbitrage Theory in Continuous Time

It's pretty well written and can get quite technical. Probably a more common reference is the two-volume set:

  1. Shreve - Stochastic Calculus for Finance I & II

The first part deals with the binomial model, which is the technique used in the Coursera course. Usually when people mention Shreve they refer to the second part, which is a lot bigger and goes into the world of continuous time. You'll find that many Master's in quantitative finance or financial mathematics will incorporate one of these two books in their curriculum.

Still, in both these books you will encounter plenty of examples where they do not go into more technical details. For that you could look at:

  1. Karatzas, Shreve - Brownian motion and Stochastic Calculus
  2. Williams - Probability with Martingales

which is pretty much written for a math audience already. In particular, pretty much all mathematical results proven and not proven in the first two books I mention, are rigorously examined in Williams. On the other hand you will not learn anything financial from this book.

Some other books worth mentioning:

  1. Joshi - The concept and practice of mathematical finance
  2. Neftci - An introduction to the mathematics of financial derivatives
  3. Baxter, Rennie - Financial Calculus
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  • $\begingroup$ I think Shreve's 2 books are an excellent read but it would help to have some rudimentary background in measure theory. But I think all the books you recommended are pretty good. I would add to the list Rebonato's Volatility and Correlation which focuses mostly on interest rate derivatives. It is also fairly technical though less so than Shreve's books. +1 $\endgroup$
    – Matt Wolf
    Commented Mar 25, 2015 at 7:43

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