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Cuchulainn
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February 7th, 2016, 1:21 pm

QuoteOriginally posted by: EscherQuoteOriginally posted by: CuchulainnAn off-topic question, maybe: how can you make pure maths (topology in all its form, measure theory, category theory) into something that is remotely computational?Off the top of my head, the ideas around persistent homology, and application of geometrical ideas to MCMC.But it's an open question as to whether you can do anything genuinely novel or useful with either of them.My gut feeling with these spaces is that they must be metrizable, i.e. topology closer to functional analysis. Ideally, a separable Hausdorff space with a countable basis.That's what Stochastic FEM has done ... an uncountable problem reduced to a Karhunen-Loeve-Fourier expansion.Then it becomes computable.
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ashkar
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February 8th, 2016, 8:58 am

I got pinged by a recruiter at fb about development role involving graph theory, algorithms etc. Also saw a lot of ML jobs on linkedin after I did a quick search. I suspect fb will pay more than £100K for senior developer. As an ML analyst at fb etc, you will also get to code quite a lot and also transition to newer technologies organically so it 'should' result in a decent long term career. I agree ML is a phase in finance. Without programming, it will become a commodity skill in next few years. Things like C++ live at-least whole generation.
 
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February 8th, 2016, 9:37 am

QuoteOriginally posted by: EscherQuoteOriginally posted by: katastrofaCould it be that your perception of English taxi drivers have something to do with the fact that you're being underpaid?Mind elaborating on that?That's all I had to say before I read your job description: "critical thought, skepticism, and attention to small details". It suggests that you're an analyst (using Excel a lot?) with a fancy job title to tickle your ego. In that case, £100k (in a good year) seems adequate.QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: EscherQuoteOriginally posted by: CuchulainnAn off-topic question, maybe: how can you make pure maths (topology in all its form, measure theory, category theory) into something that is remotely computational?Off the top of my head, the ideas around persistent homology, and application of geometrical ideas to MCMC.But it's an open question as to whether you can do anything genuinely novel or useful with either of them.My gut feeling with these spaces is that they must be metrizable, i.e. topology closer to functional analysis. Ideally, a separable Hausdorff space with a countable basis.That's what Stochastic FEM has done ... an uncountable problem reduced to a Karhunen-Loeve-Fourier expansion.Then it becomes computable.Do you have some specific problem to solve?
 
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February 8th, 2016, 3:32 pm

QuoteOriginally posted by: katastrofaQuoteOriginally posted by: EscherQuoteOriginally posted by: katastrofaCould it be that your perception of English taxi drivers have something to do with the fact that you're being underpaid?Mind elaborating on that?That's all I had to say before I read your job description: "critical thought, skepticism, and attention to small details". It suggests that you're an analyst (using Excel a lot?) with a fancy job title to tickle your ego. In that case, £100k (in a good year) seems adequate.QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: EscherQuoteOriginally posted by: CuchulainnAn off-topic question, maybe: how can you make pure maths (topology in all its form, measure theory, category theory) into something that is remotely computational?Off the top of my head, the ideas around persistent homology, and application of geometrical ideas to MCMC.But it's an open question as to whether you can do anything genuinely novel or useful with either of them.My gut feeling with these spaces is that they must be metrizable, i.e. topology closer to functional analysis. Ideally, a separable Hausdorff space with a countable basis.That's what Stochastic FEM has done ... an uncountable problem reduced to a Karhunen-Loeve-Fourier expansion.Then it becomes computable.Do you have some specific problem to solve?Moi?I think topology is a solution looking for a problem.Instead of Euler for SDE, I would like a solution using Polynomial Chaos . FDM for SDE is/feels just so wrong.I have asked this question to a few gurus; they just stare blankly at me..Somehow, we are all stranded in measure theory quicksand.Question: Can Karhunen-Loeve-Fourier expansion be used to model SDE and hence price options using MC?
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February 11th, 2016, 11:05 am

QuoteOriginally posted by: CuchulainnCan Karhunen-Loeve-Fourier expansion be used to model SDE and hence price options using MC?Sure, it's a rather standard approach.
 
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February 11th, 2016, 12:05 pm

QuoteOriginally posted by: GamalQuoteOriginally posted by: CuchulainnCan Karhunen-Loeve-Fourier expansion be used to model SDE and hence price options using MC?Sure, it's a rather standard approach.That was my hunch. Has a concise article been done here? What I did was plugging in a truncated KL expansion for W (and in particular dW) into the SDE. Then we get an ODE, a bit like FEM semi-discretization approach.
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February 12th, 2016, 10:20 am

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: GamalQuoteOriginally posted by: CuchulainnCan Karhunen-Loeve-Fourier expansion be used to model SDE and hence price options using MC?Sure, it's a rather standard approach.That was my hunch. Has a concise article been done here? What I did was plugging in a truncated KL expansion for W (and in particular dW) into the SDE. Then we get an ODE, a bit like FEM semi-discretization approach.I used that trick in my PhD thesis. In several dimensions, proving convergence tinthe limit is very tricky for anything other than a Haar wavelet expansion (see Ikeda and Watanabe's book). I asked Istvan Gyongy about it and he seemed to think you'd get convergence for many other bases.In all but a very few applications, it's hard to see what you gain by doing the expansion though. The closer you approximate the BM, the rougher your solution gets and the harder your adaptive RK scheme (or whatever) has to work.
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February 13th, 2016, 8:47 am

QuoteOriginally posted by: EscherQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: GamalQuoteOriginally posted by: CuchulainnCan Karhunen-Loeve-Fourier expansion be used to model SDE and hence price options using MC?Sure, it's a rather standard approach.That was my hunch. Has a concise article been done here? What I did was plugging in a truncated KL expansion for W (and in particular dW) into the SDE. Then we get an ODE, a bit like FEM semi-discretization approach.I used that trick in my PhD thesis. In several dimensions, proving convergence tinthe limit is very tricky for anything other than a Haar wavelet expansion (see Ikeda and Watanabe's book). I asked Istvan Gyongy about it and he seemed to think you'd get convergence for many other bases.In all but a very few applications, it's hard to see what you gain by doing the expansion though. The closer you approximate the BM, the rougher your solution gets and the harder your adaptive RK scheme (or whatever) has to work.That's interesting. I went back to some KL stuff and I have posted it hereI have not used wavelets but sine functions as orthonormal basis functions and they do give ballpark solutions. So, it seems feasible. I use Predictor-Corrector on constant step size. One question is that these basis functions do not (seem to) have compact support.(?) /* It would seem that statistical-probabilistic methods are used to solve SDE via FDM which is peculiar seeing how functional analysis would be much more powerful. Maybe I'm missing something. */
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Cuchulainn
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February 13th, 2016, 9:27 am

QuoteCan Karhunen-Loeve-Fourier expansion be used to model SDE and hence price options using MC?Sure, it's a rather standard approachStandard, where? I have not seen this in finance (but lots of Euler..).
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Gamal
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February 13th, 2016, 1:07 pm

For instance Black Karasinski.
 
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February 14th, 2016, 10:11 am

QuoteOriginally posted by: GamalFor instance Black Karasinski.Thank you, Gamal. That's a nice treatment.After page 10 of the show, instead of semi-analytical approach I plug the KL expansion into SDE to get a system of ODEs (OK, because of Wong-Zakai) solve the ODE for each path in a MC simulation.
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Gamal
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February 14th, 2016, 10:53 am

I like this research. Here in Europe I don't know any house using BK but on the other site of the pond it's more popular.
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