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Riemann zeta function finance, much used?

March 4th, 2019, 8:24 pm

I have used the Riemann zeta function a few times in practical option valuation, discrete barrier adjustments, Glasserman style  (see for example my Incomplete Guide) or the Glass paper:

http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf

see also https://www.sciencedirect.com/science/a ... 2712002567

http://www.columbia.edu/~sk75/sinica.pdf

much other use off the Riemann zeta function in finance? 

Riemann Zeta Function and the Brownian Motion of Asset Prices: Number Theory meets Quantitative Finance
 
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Pat
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Re: Riemann zeta function finance, much used?

March 19th, 2019, 2:37 pm

or the Milne extrapolation length for weakly colored noise ...
 
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Re: Riemann zeta function finance, much used?

March 19th, 2019, 8:07 pm

?
much other use off the Riemann zeta function in finance? 

RZ -> prime number -> RNG -> MC path -> the price

Not a shock.
 
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Re: Riemann zeta function finance, much used?

March 20th, 2019, 8:09 am

?
much other use off the Riemann zeta function in finance? 

RZ -> prime number -> RNG -> MC path -> the price

Not a shock.
quasi random MC? "primes ending in 1 were less likely to be followed by another prime ending in 1. That shouldn’t happen if the primes were truly random" https://www.newscientist.com/article/20 ... e-numbers/  Shocking !
 
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Re: Riemann zeta function finance, much used?

March 22nd, 2019, 11:02 am

RZ seems to have feet in two camps, namely integers and complex numbers. This means it probably misses on real analysis. Cauchy sequences of prime numbers are difficult.

https://www.boost.org/doc/libs/1_60_0/l ... /zeta.html

Connection RH and discrete dynamical systems
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf

A nice weekend exercise is to do eq. (14).
 
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Cuchulainn
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Re: Riemann zeta function finance, much used?

March 22nd, 2019, 11:46 am

That shouldn’t happen if the primes were truly random
Did someone say they were random?