ODE/PDE/SDE online courses for computational finance

[Daniel Duffy]

Thanks for the feedback!



For MFE, Parts A,B,F,G of ODE/PDE course are sufficient for a good overview and certificate.

Some middle-level calculus is needed but most students find it easy.

Normally, 2-3 months is fine to complete. I support all parts if you want to do them all. The course remains open for always.

We have an end-of-term Skype and there is an option to do a mini-project (takes a week maybe). It is up to the student if they want to do it. I recommend it if you have time.

I am personal coach, so I guide you in the learning process.

The student price is Euro 1500.



(In general, any 1st course costs Euro 1500 and any 2nd course costs Euro 995 per course.)

Online Courses :: Datasim

Online Courses

www.datasim.nl

If you are interested, can you please contact Ilona ilona@datasim.nl who will set up the admin for you.



Best regards



Daniel

 

[Daniel Duffy]

Courses are always open.

 

[Daniel Duffy]

Some one-liner remarks on how to learn ODE/PDE and apply it.

In general, we can get students with Calc3 knowledge to 1 and 2 factor PDE in finance (Fokker Planck, Black Scholes, Hull White, CIR, XVA etc.) in about 2 or 3 months.

Some objective criteria to measure the quality of student solutions:
1. Flow: readable step-by-step solution from input to output.
2. Completeness: Rigorous solution to the problem; no gaps and no stone unturned.
3. Accuracy: multiple solutions to the problem.
4. Scope and initiative: taking it beyond the current problem (e.g. extended examples from Duffy’s books).
5. The percentage of numerics/Python code to support the maths.

Part A is initial value problem (IVP) for 1st order ODEs. The independent variable is time t.
Part B is boundary value problem (BVP) for 2nd order time-independent convection-diffusion-reaction ODEs. It is a vital part and basis for F (F = A + B) and G == F in the context of finance PDE.

Essential skills in B:
a. ODE in several forms (adjoint/conservative, non-conservative).
b. Domain transformation (and truncation).
c. The Fichera function (a kind of recipe).
d. Instead of c, use well-posedness/energy inequalities approach (2022 book,section 25.4), arrive at conclusion BC yes/no from 1st principles (See thesis by Fei Lu).
e. ODE implemented by FDM (stability, accuracy etc.)
f. Some forms of a more suitable to different methods: FEM (see Duffy 2006, Appendix 2), MOL (Duffy 2022, chapter 20).

 

[Daniel Duffy]

@Ken Abbott

 

[Daniel Duffy]

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