Hi Chris (et al) It sounds like you've got a lot on your plate, but we apparently have some common interests.
When the smoke settles for you and you're looking for some night time reading (i.e. cure for insomnia), you might have a look at some of my old papers: - - Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance <https://phorgyphynance.files.wordpress.com/2008/06/blackscholes.pdf> I'm pretty sure I am the first person to apply NCG to finance :) I followed that one up a couple years later with a more concrete application for practitioners: - Financial Modelling Using Discrete Stochastic Calculus <https://phorgyphynance.files.wordpress.com/2008/06/discretesc.pdf> Discrete stochastic calculus provides a kind of meta algorithm. It is an > algorithm for generating algorithms. > If that doesn't cure your insomnia, this one surely will: - Discrete Differential Geometry on Causal Graphs <http://arxiv.org/abs/math-ph/0407005> The above is a follow-up to work started in my dissertation at UIUC: - Differential Geometry in Computational Electromagnetics <https://phorgyphynance.files.wordpress.com/2008/06/final.pdf> It was still a work in progress, but its not easy creating an entirely new framework for scientific computation, so I guess they thought it was enough :) Anyway, I mention this because discrete stochastic calculus (DSC) would have a completely natural implementation in Julia using concepts similar to automatic differentiation to give you things like Ito formula for free. If I could clone myself, I would develop that, but I'm a "seniorpreneur", i.e. industry veteran (a.k.a. old man) working on my third FinTech startup, so it is on the back burner for now :) My friend, John Baez, changed his academic passion from quantum gravity to environmental science a few years ago, which motivated me to start applying DSC to problems in fluid dynamics with some very cool result for Burgers and Navier-Stokes equations (all unpublished). You can find a bunch of info about that here <https://phorgyphynance.wordpress.com/2011/10/28/network-theory-and-discrete-calculus-introduction> . Cheers PS: Just before hitting "Send", I notice several of the links in my last reference are broken, which tends to happen after more than 5 years :), so here is one that should be good for Burgers stuff: - Discrete Burgers equation revisited <https://forum.azimuthproject.org/discussion/comment/4993> The important quote: > I did not do much more with the discrete Burgers equation for reasons > similar to John's. As far as I am concerned the problem is solved. I wrote > down and implemented in code an algorithm having the magical property that > the accuracy gets BETTER the longer you simulate. You cannot ask for more > than that. Finally: - Towards Navier-Stokes from noncommutative geometry <https://forum.azimuthproject.org/discussion/comment/4204> Fun stuff! I miss doing research like that :)
