Learning mathematical plumbing v/s an engineering view

[Quasar Chunawala]

Dear all,

I hope you are all faring decently.

To gain a general knowledge of probability; to polish my technical skills, I am reading some basic material and solving problems through two texts -

(1) Probability theory by the Croatian born probabilist William Feller.
(2) Analysis by Tao.

Taking some LaTeX notes (see attached).

At this point, I am equally interested to dive into some basic mathematical finance, to see what's going on intuitively. So, I am indulging in reading

(1) Financial Calculus by Baxter, Rennie.
(2) Stochastic Calculus (Discrete & continuous time) by Shreve.

For those, who've read Baxter and Shreve's books, I wanted to ask, how accessible is a practitioner's book such as the one by Piterbarg, if I work through Shreve? Is that a big leap?

My understanding is, not everyone who joins a financial engineering school necessarily has a training in graduate level probability. So, how do they master the discipline? Are there specific courses that you are required to take? I also read up here - MTH 9831 Probability and Stochastic Processes for Finance I.

I'd really appreciate your feedback.

Thanks,
Quasar.

 

[Qui-Gon]

Hey Quasar,

While I haven't read Baxter & Rennie, I have worked through almost all of Shreve 1 and the first 6 Chapters of Shreve 2 (this forms the core of the book; I would also check out Chapters 9 and 10 as this treats fixed income applications) in some detail. Judging by the contents of Ch. 1 of Piterbarg's Volume 1, I think the Shreve series, really just Shreve 2 in fact, makes for sufficient preparation. A book I highly recommend to read alongside Shreve 2 is Kuo's "Introduction to Stochastic Integration". Kuo's text supplements the sometimes lacking mathematical rigor of Shreve 2; the first 5/6 chapters of Kuo were a goldmine for me while learning from Shreve 2, and I think they will be for you as well given it seems you are taking time to learn real analysis which makes Kuo even more rewarding. A book to perhaps have partnered with Piterbarg is "The Volatility Surface" by Gatheral as it seems Piterbarg treats local and stochastic volatility models, thus Gatheral's text could help supplement any background you are lacking upon reading Shreve.

I cannot answer your second question as I myself am a MFE aspirant. I imagine MFE programs have gotten very good at packaging the necessary graduate level probability for quantitative finance into their curriculum, even if it is surface level at times.

 

[KillingField]

Andersen and Piterbarg summarise the needed background and results from measure theory in the first 20 pages, and after that you'll never need to think about sigma algebras again. Even Baxter and Rennie is enough of a background to tackle Andersen and Piterbarg - the focus is not on mathematical rigour, and if memory serves, the authors themselves say as much at the opening of the book.

 

[Quasar Chunawala]

Thank you so much @Dexter Dysthe and @KillingField - this is much helpful.