# Text on Probability Theory applied to Actuarial Science

I am a senior undergraduate who has passed the first three actuarial exams on probability (P), financial mathematics (FM), and models for financial economics (MFE). I am working on passing the life contingencies exam in April.

For my final semester as an undergraduate, I am doing an independent study to learn about measure-theoretic probability theory in the context of actuarial science. I am especially interested in learning the theory behind Ito calculus and the proof of the Black-Scholes equation and formula, rather than just doing routine calculations using these formulas (like in exam MFE).

The current plan is to start off with A Probability Path and Adventures in Stochastic Proccesses both by Resnick, but none of these cover Ito calculus. They touch on Brownian motion and martingales for a little bit, but not very much of it.

I have taken two semesters of real analysis (we covered everything up to complete metric spaces and integration and differentiation in $\mathbb{R}^n$) and will be taking my second semester in abstract algebra (vector spaces, group actions, Sylow $p$-groups, and some other stuff I don't know about). Is there a text that we can use during this independent study that would be accessible to me that pertains to Ito calculus and its applications to finance (and/or actuarial science)?

Edit: Two texts that I have found in my research are Brzezniak and Zastawniak and Øksendal. Does anyone have a particular preference of one of these over the other? Are there any other texts you would recommend?