By Pankaj Mani
9th Jan 2024
The Celebrated famous Identity by Indian Legend Ramanujan Summation in Mathematics having wide deep applications across the fields. This is one of the most important mysteries of science.
Sum of all the Natural Numbers upto infinity
1+2+3+4+........♾️(Infinity)= -1/12
The above peculiar identity is deeply linked with the Celebrated Riemann Zeta Function(named after legend German mathematician Bernhard Riemann and the correspondingly, the most important unsolved problem in pure mathematics Riemann Hypothesis for around one and half centuries. This Ramanujan Summation has crucial applications in Quantum Field Theory etc.. Physics as well. Riemann Zeta Function is also interestingly involved in Option Pricing
And more importantly here, this Riemann Zeta Function linked to the Ramanujan’s famous identity is also deeply linked to the Brownian Motion, the Foundational Infrastructure of Mathematical (Quant) Finance !
Such is the intriguing depth and beauty of Financial Markets-Number connection involving trillions of dollars of quant investments globally ! It also leads to the introspection how Mathematics and Human Sense of the world we live in, are also deeply linked ! One needs to explore how? !
References:
1)https://www.nytimes.com/2014/02/04/science/in-the-end-it-all-adds-up-to.html
2)https://onlinelibrary.wiley.com/doi/10.1111/1467-9965.00035
Pricing of Options : Broadie, Glasserman and Kou 1997)
3)https://link.springer.com/chapter/10.1007/978-3-0348-8954-4_2
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