Graeme, this is a great list. 

-t.

Applied maths is better for quant finance.  But for trading, particularly vanilla trading, there's a case for stats, to help with identifying patterns under noise and uncertainty.  Plus stats is a rare skill in finance since exotics modeling is considered sexier.

Of course, in an ideal world you wouldn't make it either/or, but would do as much as posible of both.

The list wasn't supposed to be ordered in any way....

I guess in some specialisations the stats would be far more important. But that wasn't supposed to be my point - the list was supposed to be what would be helpful as a priori knowledge for formal study (and not an opinin on what aspects of formal study are relevant and which not). For example, if you have my 6. then you cover CAP-M in your studies while watching the game on the box, if not, it could take you weeks.

Once you are working things might move around significantly. If you are in any sort of data mining area I guess the stats would become crucial. In other areas most stats might be irrelevant.

mj, do u think pure math could be relevant?

not directly relevant, but relevant to the extent that it is mental weightlifting.  is it relevant to pump iron if you want to play football? 

by the way, I've been noticing that a lot of global macro guys have studied philosophy.  of course, to be a successful global macro trader it is relevant that the degree is from Harvard, Yale, or Princeton.

Yeah, cool then. But still, my 2-pesos impression is that the more time one put on thinking about commutative diagrams, schemes, varifolds, semimartingales and all the fancy-shmancy stuff of "higher" pure math, the less he is likely to feel comfortable with "dirty" computational issues (which constitute 99.99% of applicable math, i guess).  I do not contest the great mental fitness exercise of these studies, obviously.

Anyway, interesting considerations...

> Good list. > I wish i knew the list when I was studying Financial math. > ... also I think for 5. numerical PDE you want to focus on FDM instead of FEM.

Yes, Finite Element Method (FEM) is a sledge hammer for finance problems for a number of reasons. It was created by Courant/Synge for structural time-independent problems with complicated geometry. FEM can be applied to parabolic problems but is no added value.

With FEM, it is useful to know Hilbert and Sobolev spaces. 

A useful application of FEM is modelling black-body radiation problem in an irregularly shaped cathode ray tube with Boltzmann radiation boundary conditions. It is a heat equation.

For fluid dynamics, FVM and FDM are more usual.

The theory behind FEM is beautiful but go for FDM in this case.  FEM is a kind of applied Functional Analysis.

A hybrid model in finance I have seen is the PIDE jump models where FDM was used for the PDE part and FEM for the integral (non-local) part by using the Galerkin method. That was a spark of genius by the guy who did it.