Serving the Quantitative Finance Community

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Cuchulainn
Posts: 64971
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### Re: Is the type of mathematics found in finance limited?

It could have been worse; what if it had been Rocky.
Last edited by Cuchulainn on July 17th, 2018, 2:57 pm, edited 1 time in total.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

ISayMoo
Posts: 2368
Joined: September 30th, 2015, 8:30 pm

### Re: Is the type of mathematics found in finance limited?

They were discussing the next Terminator movie. There's no better warning about what happens when we let the machines help us!
This ship has sailed long ago.

Paul
Topic Author
Posts: 11373
Joined: July 20th, 2001, 3:28 pm

### Re: Is the type of mathematics found in finance limited?

I know! (Although ships have been known to change direction!)

Cuchulainn
Posts: 64971
Joined: July 16th, 2004, 7:38 am
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### Re: Is the type of mathematics found in finance limited?

They were discussing the next Terminator movie. There's no better warning about what happens when we let the machines help us!
This ship has sailed long ago.
You're gonna need a bigger boat. And possibly a different cargo.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

katastrofa
Posts: 10249
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Is the type of mathematics found in finance limited?

Did Arnold say "Hasta la vista, baby!" for goodbye?

Alan
Posts: 10710
Joined: December 19th, 2001, 4:01 am
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### Re: Is the type of mathematics found in finance limited?

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.

Collector
Posts: 4926
Joined: August 21st, 2001, 12:37 pm

### Re: Is the type of mathematics found in finance limited?

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).

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!
Well, 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).
"…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." Schrodinger

biology, chemistry and finance are all branches ultimately springing out off physics, as long as fundament is incomplete, the branches cannot be fully trusted! Go to the root and trim the branches!

Hasta la vista, babies!

Cuchulainn
Posts: 64971
Joined: July 16th, 2004, 7:38 am
Location: Drosophila melanogaster
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### Re: Is the type of mathematics found in finance limited?

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.
Why stop there? Why not go straight to the next level Sedonians which have non-trivial zero divisors. That's even more exciting.

I think these people are taking the law into their own hands. Juggling with algebraic symbols?

You can't define Cauchy sequences in octonian space, what?
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

fin79
Posts: 2
Joined: January 21st, 2021, 9:10 pm

### Re: Is the type of mathematics found in finance limited?

I wonder why there is not much interest in applying Chaos Theory to finance, in a way Chaos theory deals with randomness too.

Alan
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Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: Is the type of mathematics found in finance limited?

Try "The Predictors" by Thomas Bass

bearish
Posts: 6626
Joined: February 3rd, 2011, 2:19 pm

### Re: Is the type of mathematics found in finance limited?

Mandelbrot himself wrote a book on the topic some 15 years ago. “The (mis)behavior of markets”.

Paul
Topic Author
Posts: 11373
Joined: July 20th, 2001, 3:28 pm

### Re: Is the type of mathematics found in finance limited?

And it was very popular in finance in the late ‘80s and early ‘90s.

But apart from all those…

Cuchulainn
Posts: 64971
Joined: July 16th, 2004, 7:38 am
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### Re: Is the type of mathematics found in finance limited?

Mandelbrot himself wrote a book on the topic some 15 years ago. “The (mis)behavior of markets”.
I met the great man twice

1. In 1978 at a numerical analysis conference in Nijmegen. He was promoting his book on fractals + complimentary copies to key speakers. Most were bemused. He promised me a copy ...
2. At one of Paul's book jamborees at the financial bookshop on that busy Bishopsgate corner. Personalised signed copy. I gave it to my friend Exsan.

Chaos Theory is a bit like AI or parts of physics... in the twilight zone, a kind of Cinderella subject. Some love it. Lyapunov is >>
Maybe Hurst exponent and rough vol models might save it?
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl