The proof of Crank-Nicolson montonicity (for a small enough time-step) is in Pooley et al. "Numerical Convergence Properties of Option Pricing PDEs with Uncertain Volatility". A different more general proof is also in Boley & Crouzeix "Conservation de la positivité lors de la discrétisation des pro...

The proof of Crank-Nicolson montonicity (for a small enough time-step) is in Pooley et al. "Numerical Convergence Properties of Option Pricing PDEs with Uncertain Volatility". A different more general proof is also in Boley & Crouzeix "Conservation de la positivité lors de la discrétisation des pro...

Why not just keep out marketing/sales spin from your posts?

Corrected, thank you for the quote, you are right, it was misplaced.

Why all the hullaboo in ML circles on SVM? It is just a special finite-dimensional case of a specific (hyperplane!) separation theorem in (geometric) Functional Analysis..It has been used in many fields for a long time, e.g. geometric modelling etc. https://en.wikipedia.org/wiki/Hyperplane_separati...

And I don't see how Crank-Nicolson can be made monotone. We are waiting on a proof. You will have it when we will publish our paper. To be honest, all is written, but I am not in a hurry to publish our algorithms, and I am taking time watching flies around. But we will, free of research taxes, for ...

A realistic first case is to produce monotone schemes for 2-factor Heston PDE with non-zero correlation. This is an open problem AFAIK. @Cuchullain, we did 2 factor Heston PDE with non zero correlation with our schemes, and it is published in CRAS - 2017. There is no interest for me to do this expe...

@Cuchulainn Hello. I will try to read all this, I might not do this this week end. However here what I think today : - We can test exponential fitting in a high-dimensional setting : you could toy with any stochastic process, regardless of the number of underlyings (high dimensional), any size of po...

More coherence is a good idea. I reckon kats can handle the technical level. I hate blogs. LI is FB 2.0, it's junky. Use SSRN or arxiv. Coherence comes after knowledge and understanding of problems. It's not enough to put technical terms together like my AI text generators do. BTW, JohnLeMAI dice (...

I was thinking to what Katastrofa was saying : " You can also see that the number of the model parameters grows with the number of datapoints". the complexity of a Support Vector Machine is LINEAR in the number of datapoints, as are NNs: same methods, but one is understood and masterized, and the ot...

or fun numerical experiments, Eh? These are not supposed to be fun! What's your secret? Unfortunately, I find my job fun and exciting. Am I sick? I toy a lot with math or tech: a tribute to sex pistols , a universal digital bill of rights  (actually an information system following it), a model for ...

More coherence is a good idea. I reckon kats can handle the technical level. I hate blogs. LI is FB 2.0, it's junky. Use SSRN or arxiv. I am pushing on arxiv or SSRN pre-prints, joined with submission to peer reviewed papers. In these posts, I don't want to go that far : simple scientific message, ...

Don't take it personally. Just improve. Do this in latex. ltr] V ( S 0 , 0 ) = ( F ( S 0 , 0 ) − K ) e − r T V(S0,0)=(F(S0,0)−K)e−rT  What the hell is it? I think this is bad copy / paste from the OP (Owner of Post) : " At the end of the finite difference scheme, to obtain the value of the option a...

JohnLeM,
Your latex notation needs some seeing to.

Google translated seeing to as "the act of hitting someone repeatedly and hard".
Wow, do I really deserve a spank ? Which notation is awful ?

No problem, it is a public forum, and I am sorry if my posts are too technical, conflictual or not understandable. Obviously I am at your disposal, or at the disposal of anyone that wish to further discuss these matters, that could have a real impact on those who are investing in Neural Network tech...

And a folder for DKE "deep kernel engineering". Only a matter of time.

I thought about it and created one. But finally this "deep kernel engineering" folder has moved and merged into the folder "kernel engineering" deep neural networks told me that they feel very comfortable inside !