How are ODEs/PDEs/Measure theory introduced in MSQF/FE programs

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Outside of Rutgers and a few other programs ODEs and PDEs aren't a prerequisite. Do FE/QF related graduate programs introduce them and apply them to finance (removing a lot of nuance of the physical application)? The same goes for measure theory, but that is typically a graduate course, though I have not yet seen it as a course at these programs, which I have the same question as before.
 
Solution
Measure theory I've never seen covered in a financial engineering program. ODE and PDE material is very specific to solve the PDEs you face in quant finance such as the Black Scholes PDE and its extensions.
No program will cover measure theory. These programs are terminal programs with the main goal of getting their students into good jobs. Thus, the curriculum will never be that rigorous.
 
To really understand measure theory, 4 year honours undergraduate maths courses are needed. Been there, done that. My Prof was a PhD student of William Feller at Princeton at the the time, so I got it from a good source. terse stuff..

It's kinda cruel subjecting (unprepared) MFE students to MT.

// I always found MT rather lacking in real applications.
 
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To really understand measure theory, 4 year honours undergraduate maths courses are needed. Been there, done that. My Prof was a PhD student of William Feller at Princeton at the the time, so I got it from a good source. terse stuff..

It's kinda cruel subjecting (unprepared) MFE students to MT.

// I always found MT rather lacking in real applications.
Any books you can recommend good sir?
 
Construction of stochastic integrals is inherently measure theoretic in nature, probability theory done at the graduate level is measure theoretic. While not a formal treatment, Shreve 2 does introduce sigma fields, pointwise convergence almost everywhere, Lebesgue integrals, etc. — basic measure theory topics, sure, but nonetheless it is there.
 
Construction of stochastic integrals is inherently measure theoretic in nature, probability theory done at the graduate level is measure theoretic. While not a formal treatment, Shreve 2 does introduce sigma fields, pointwise convergence almost everywhere, Lebesgue integrals, etc. — basic measure theory topics, sure, but nonetheless it is there.
The treatment is too short..
Do you know the books by Kloeden and Platen? you should.
These are definitive!
 
I recently tried to learn few pre-requisites with the objective of picking up stochastic calculus.

I found the presentation of the basic ideas in Capinski to be particularly enjoyable - null sets, outer-measure [imath]\mu^{*}(A)[/imath] as the infimum of lengths of all coverings of the set [imath]A[/imath], and that its subadditive. It motivates, that its fair to demand that a length function at the very least be countably additive. All of this just using first principles, just in chapter 2 of the book. Little proofs left as exercises were fulfilling.

Other than that, I understood the key ideas in probability theory - BCL, convergence of RVs from the lecture notes and videos in this playlist.
 
Just arrived! Handsome bookie for sure.

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Paul Halmos was Hungarian.
I met him a few times at some lectures he gave in the 1970s in Trinity College.


  • 1942. Finite-Dimensional Vector Spaces. ...
  • 1950. Measure Theory. ...
  • 1951. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. ...
  • 1956. Lectures on Ergodic Theory. ...
  • 1960. Naive Set Theory. ...
  • 1962. Algebraic Logic. ...
  • 1963. Lectures on Boolean Algebras. ...
  • 1967. A Hilbert Space Problem Book.

 
Paul Halmos was Hungarian.
I met him a few times at some lectures he gave in the 1970s in Trinity College.


  • 1942. Finite-Dimensional Vector Spaces. ...
  • 1950. Measure Theory. ...
  • 1951. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. ...
  • 1956. Lectures on Ergodic Theory. ...
  • 1960. Naive Set Theory. ...
  • 1962. Algebraic Logic. ...
  • 1963. Lectures on Boolean Algebras. ...
  • 1967. A Hilbert Space Problem Book.


I wonder what was in the water in Hungary in those days to produce so many geniuses. :)
 
Cornelius Lanczos once offered us undergrads a challenge in Dublin; generalise Radon-Nikodym theorem to complex variable case.
 
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