It could have been worse; what if it had been Rocky.
This ship has sailed long ago.They were discussing the next Terminator movie. There's no better warning about what happens when we let the machines help us!
You're gonna need a bigger boat. And possibly a different cargo.This ship has sailed long ago.They were discussing the next Terminator movie. There's no better warning about what happens when we let the machines help us!
"…living matter, while not eluding the "laws of physics" as established up to date, is likely to involve "other laws of physics" hitherto unknown, which however, once they have been revealed, will form just as integral a part of science as the former." SchrodingerWell, OK. By the same rationale, I guess one could say all of biology and chemistry is simply applying fancy techniques to the same boring equation (non-relativisitic Schrodinger equation).For a moment I thought these were good examples. Who doesn’t like an eikonal equation?! But really these just come from applying different techniques to the usual type of governing equation. I don’t think fancy techniques applied to boring equations quite satisfies me, I’m afraid!There is a fair amount of interesting math (at least to me) in my second volatility book. Some examples:
1. I took one course in general relativity as a senior at Caltech. But, I think I learned more Riemannian geometry in doing my chapter on "Advanced smile asymptotics" then I ever learned in that course. If non-linearity is your criterion for "interesting", you get that in the interplay between the eikonal and geodesic equations.
2. I have a chapter on "Spectral theory for jump-diffusions". This is a relatively undeveloped area -- as the finance operators are typically non-self-adjoint. (99% of textbook stuff is for self-adjoint operators). I came to appreciate some parts of functional analysis much more in writing this chapter.
3. Continuous-time inference for diffusions yields some interesting puzzles, esp. when boundary behavior is involved; for example, with slowly-reflecting diffusions or even just the square-root volatility process. I came to appreciate Girsanov theory more from writing that one. As part of that chapter, you may remember this nice thread (although many of the equations seem to be lost).
Why stop there? Why not go straight to the next level Sedonians which have non-trivial zero divisors. That's even more exciting.All right people, here you go
The next step is obviously [$]\mbox{Octonion Finance}^{TM}[$]
It's clear that finance is *not* always commutative:
(Entity declares bankruptcy) x (Sue entity) [$]\not=[$] (Sue entity) x (Entity declares bankruptcy).
But, for Octonion Finance, as explained in the link, you need to show why finance is also not always associative over some operation. Fortune and glory, kids, fortune and glory.
I met the great man twiceMandelbrot himself wrote a book on the topic some 15 years ago. “The (mis)behavior of markets”.