Geometric Arbitrage Theory (fibre bundles & sht)

constantine · Post by **constantine** » Sat Jan 22, 2011 11:40 am

I can't tell if this is extremely important or extremely academic.

Any opinions from real traders appreciated.

http://arxiv.org/abs/0910.1671

We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to:

- Write arbitrage as curvature of a principal fibre bundle.

- Parameterize arbitrage strategies by its holonomy. - Extend the Fundamental Theorem of Asset Pricing by a differential homotopic characterization for both complete and not complete arbitrage free markets.

- Characterize geometric arbitrage theory by five principles and show they they are compatible with the classical theory of stochastic finance.

- Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where:

--> Arbitrage is allowed but minimized.

--> Arbitrage is not allowed.

- Prove that the no-free-lunch-with-vanishing-risk condition is equivalent to the existence of a utility maximizer.

rod · Post by **rod** » Sat Jan 22, 2011 9:08 pm

Frankly, I don't think that "real traders" know Differential Geometry. A few of them, perhaps. Arbitrage as curvature of a principal fibre bundle??? Sounds exactly the kind of stuff Tsar Nonius would write...

Maggette · Post by **Maggette** » Sat Jan 22, 2011 9:43 pm

Hej,

maybe you are interested:

https://nuclearphynance.com/Show%20Post.aspx?PostIDKey=870

and

https://nuclearphynance.com/Show%20Post.aspx?PostIDKey=99478

Cheng · Post by **Cheng** » Sun Jan 23, 2011 8:59 am

This sounds like N is back in town.

constantine · Post by **constantine** » Sun Jan 23, 2011 9:02 am

Can you point me to a typical post of his/hers? I don't get what you mean.