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How mandatory is it to have PDE courses in undergrad to apply for MS QF.

jessefreitag

Joined
10/17/21
Messages
17
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13
I’m an Applied Math and Economics major from Stony Brook and we do not have a PDE course available for undergrad. However, I did take ODE and we touched upon PDE’s and my Quant Finance course I am taking right now is teaching Brownian motion, BSM model etc.
Thanks.
 
Not sure about programs associated with Math departments but for MSFE it is not required. If I had to guess about 50% of current Columbia MFE students have PDE knowledge. In my program you do not need to know how to solve a PDE by hand. ODE's however are a required prerequisite knowledge.
 
The Courant Math Finance looks for students with strong math skills. Although taking an undergraduate course in ODEs and/or PDEs helps, we don't consider it essential.
 
My own background has been heavily influenced by pure maths, numerical analysis and PDE research and industrial work since 1973. In those glory days of oii and gas, semiconductors and engineering using FEM and FDM had lots of jobs, but you needed Fortran on mainframes.

My PhD was on PDEs which I later realised subsumed Black Scholes PDE. What a coincidence.
BTW ODEs are also very important.

For a number of historical reasons. much of my PDE work was influenced by research from the former USSR.

I have just publihed my new PDE book for future generations. :)

www.wiley.com

Numerical Methods in Computational Finance: A Partial Differential Equation (PDE/FDM) Approach

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices...
www.wiley.com www.wiley.com
 
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CourantMathFinance said:
I agree that it's very unusual for a math or applied math department not to offer an undergraduate PDE course.
Click to expand...
I have taken a Differential Equations course that used half the semester on PDE, and there are some courses that use stochastic calculus, but there isn’t a course explicitly named “Partial Differential Equations”.
 
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Where will the rocket scientists come from???

Early 20th century things started going wrong

Mathematical Physics experienced a schism into Mathematics and Physics ... beginning of the end.

The mathematicians fell in love with symbols and the physicists lost touch with reality. Grosso modo.
 
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jessefreitag said:
I have taken a Differential Equations course that used half the semester on PDE, and there are some courses that use stochastic calculus, but there isn’t a course explicitly named “Partial Differential Equations”.
Click to expand...
what was the other half? ODE?
 
Something that is not widely known ..
There is a third way between searching for an explicit solution (a big favourite!) and a numerical solution

In mathematics, the qualitative theory of differential equations studies the behavior of differential equations by means other than finding their solutions. It originated from the works of Henri Poincaré and Aleksandr Lyapunov. There are relatively few differential equations that can be solved explicitly, but using tools from analysis and topology, one can "solve" them in the qualitative sense, obtaining information about their properties.[1]

Exampe: 2 factor options (exchange, spread etc.)

1. Analytic solutions are possible, but each derivative payoff ==> a new round of maths
(and often there is no easy analytic solution, what then?)
2. PDE can handle all the cases in 1 in one swoop ... each payoff is just an inital condition. Then we solve all pdes with ONE fdm.
Write the PDE and FDM c;lasses once and instantiate them as often as you like.
 
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