Mathematics for quantitative finance (Reitano)

[Ramanidis]

I am going to undertake a mfe program next year. And I want to know, how "mathematical" is quants work is. I came over Robert Reitanos book (http://www.amazon.com/Introduction-Quantitative-Finance-Math-Tool/dp/026201369X), and it is just pure math in its pure form. Is it essential for a quant to acquire knowledge of such deep mathematics? Would you recommend a person to consume this book to succeed in mfe program and future quants work?

Thank you!

 

[Jayanthan]

From the section, "Quant Education" :
Educational Advice:
https://www.quantnet.com/forum/education-advice.78/

Books:
https://www.quantnet.com/forum/books.37/

 

[bigbadwolf]

Would you recommend a person to consume this book to succeed in mfe program and future quants work?

Avoid the book. It is stupidly written. Get hold of books like Dan Stefanica's Primer for the Math of Financial Engineering, Luenberger's Investment Science, and Wilmott's Intro to Quant Finance.

 

[Ramanidis]

Avoid the book. It is stupidly written. Get hold of books like Dan Stefanica's Primer for the Math of Financial Engineering, Luenberger's Investment Science, and Wilmott's Intro to Quant Finance.

Thank you Any particular reason why it is badly written? Too many "additional useless info" or what? Also, is there a PDF copy available of Dan Stefanica? I've been searching quite long for this. Like to read before buying a copy.

 

[bigbadwolf]

Any particular reason why it is badly written? Too many "additional useless info" or what?

Didn't say it is badly written -- it seems to be written in the same slick style of pure math books -- definition-lemma-theorem-corollary. It's stupidly written. That style and that content is just the thing you don't need. Any time you hear terms like "sigma algebra," "Banach space," and so on, you should -- to paraphrase the late and lamented Hermann Goering -- reach for your revolver. It's what you don't need. Pay attention to the finance and the coding and enough of the math so that you understand what's going on. The pure math approach is wrong, the approach of engineering and physics is the right one. Bourbaki is dead.

Also, is there a PDF copy available of Dan Stefanica? I've been searching quite long for this. Like to read before buying a copy.

It's not expensive as books go. Buy it. And the solution manual.

 

[Daniel Duffy]

Bourbaki is dead.

RIP

The pure math approach is wrong.

I would not go so far. You need pure maths to temper the - sometimes unfounded - assumptions made in applied/engineering/ad-hoc mathematics.

 

[bigbadwolf]

I would not go so far. You need pure maths to temper the - sometimes unfounded - assumptions made in applied/engineering/ad-hoc mathematics.

Pure math never tells the physics and engineering people they've been wrong -- in practice it always invents justifications for what they've invented and used on an ad-hoc basis. The Dirac delta function and the subsequent theory of distributions is a prime example. Feynman's condescending attitude towards pure math is in my opinion the right one. What the pure math people tend to do is to take some intuition from the physicists and dress it up in the baroque formalism of definition-lemma-theorem-corollary until the motivating intuition is smothered.

 

[Daniel Duffy]

Pure math never tells the physics and engineering people they've been wrong -- in practice it always invents justifications for what they've invented and used on an ad-hoc basis. The Dirac delta function and the subsequent theory of distributions is a prime example. Feynman's condescending attitude towards pure math is in my opinion the right one. What the pure math people tend to do is to take some intuition from the physicists and dress it up in the baroque formalism of definition-lemma-theorem-corollary until the motivating intuition is smothered.

That's maybe a reason Feynman could never become a mathematician.

Dirac's distribution is too weak, mathematically. It's real ad-hoc in that sense. It took Schwarz, Sobolev and others to establish the foundations of Distribution Theory and then apply it, e.g. finite element.

Ex PDE

1. Prove PDE has a unique solution in certain Sobolev space
2. Prove weak solution of 1 exists and is unique
3. Prove weak solution == solution in 1
4. Find approximate solution to ws in 2. Prove existence and uniqueness.
5. Program solution of 4 using FEM.


Most of this is (applied) functional analysis.