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Wikipedia states the 2021 Breakthrough Prize in Mathematics announced in September 2020 was made to Martin Hairer - "For transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations." Please explain what the breakthrough was in intuitive terms as the press articles gloss over it.

Does the result have any relevance to Quantitative Finance?

rupert
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  • Martin Hairer seems to be active only on mathoverflow. He doesn't have a Quant Finance stack exchange account, so doubt he'll answer your question here. Also, he doesn't seem active on math SE either... – Jan Stuller Feb 10 '21 at 14:15
  • PS: there is an interview with Martin at the bottom of the Imperial website here. Haven't listened to it yet, but it should give some intuitive explanation about what he got the prize for. – Jan Stuller Feb 10 '21 at 14:29
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    This question would be better asked on math overflow or math stack exchange. Hairer's work is not immediately relevant to quantitative finance, although it would be very cool if someone discovered an application (that actually worked!) – rubikscube09 Feb 10 '21 at 14:45
  • Here was Martin's contribution on the Feller condition on maths stack exchange that I spotted earlier today mistakenly thinking I was on Quant Finance SE: https://mathoverflow.net/q/280388 I believe Feller condition is relevant to the CIR model although not to Heston. – rupert Feb 10 '21 at 15:09
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    Please see page 7 in the attached for a nice intro to the topic: https://arxiv.org/pdf/1303.5113.pdf – Magic is in the chain Feb 10 '21 at 17:41
  • @rupert yes the Feller condition is relevant to make sure that interest rates don't go negative in the model. But look where we are now:) Possibly not so relevant anymore. – rubikscube09 Feb 10 '21 at 18:06
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    @rubikscube09 it works with instantaneous variance in the Heston model too, and var defo shouldn't go negative – James Spencer-Lavan Feb 10 '21 at 20:50
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    In some (very oversimplifying) sense Hairer's theory is a multidimensional generalization of that of rough paths. Not an expert, but there seems to be applications to finance for the theory of rough paths as suggested by the publications of its inventor https://www.maths.ox.ac.uk/people/terry.lyons As for the more general (and more recent) theory developed by Hairer, some people are currently working on possible financial applications, see in particular https://people.math.ethz.ch/~jteichma/ – Abdelmalek Abdesselam Feb 10 '21 at 23:46
  • an example of work about regularity structures in math finance: https://onlinelibrary.wiley.com/doi/full/10.1111/mafi.12233 – Abdelmalek Abdesselam Feb 22 '21 at 20:48
  • Brownian Castles and the Yang-Mills Millennium Problem with Martin Hairer (Fields Medal 2014) https://www.youtube.com/watch?v=4jR8Sg4PYAA – rupert Mar 10 '21 at 19:55

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