Thank you for your answers, I took some time to think about it and now have the feeling I'm beginning to understand what you mean.(i) When I asked the question, I had more traditional markets in mind (like for swaptions, where HFT isn't important afaik). Here, I guess "making money" always corresponds in a way to "seeing better in the future". That is, it doesn't matter whether a model is much more complicated, but only whether it better describes the conditions into which the market is going to evolve (... and the same holds for the set of free parameters you need to adjust in any model). This is what Alan means by "insight", I guess ... and this seems not directly related to a "god-solver", as it's not about the solution but rather about the model. (ii) The benefits of the speed component of the "god-solver" is more or less obvious -- when speed matters (as in HFT), being the fastest is a good thing. However, as before, this doesn't mean you can better look into the future. So again one needs a valid strategy, and there seems to be no cases where you directly gain just because you have an astronomical solution method (at least unless you supply it with an "astronomical trading strategy").When I asked the question my hope was more or less that there are such situations in the market where computational power -- and only computational power --matters. Now, after the input by you and some thoughts, I'd rather think that this is never the case -- great computational power doesn't relieve you from using a good trading strategy. Conversely, good strategies might give you an edge, and possibly these strategies might require heavy computations.QuoteOriginally posted by: CuchulainnQuoteNow, let's assume you had available an astronomical solution method, which gives you the exact solution of any stochastic model (for an arbitrary number of factors) and that in milli-seconds. Like a closed solution to the stochastic Navier-Stokes equation?I was thinking more in numerical terms, but why not? The strategy to make money here is also simple: just get you the millenium price million