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March 13th, 2015, 8:27 pm
Forum: Technical Forum
Topic: Density of Stochastic Differential Equations with Stochastic Calculus of Standard Deviations
Replies: 71
Views: 11770

### Density of Stochastic Differential Equations with Stochastic Calculus of Standard Deviations

<t>Thank you for your answer and the short summary. Those ideas really sound interesting to me (--or, at least the first one, i.e. to use Ito iteratively for the coefficient functions ... whereas the second one, Q-coordinates, I haven't understood so far). So I will definitely give the (new) paper a...
March 13th, 2015, 1:16 pm
Forum: Technical Forum
Topic: Density of Stochastic Differential Equations with Stochastic Calculus of Standard Deviations
Replies: 71
Views: 11770

### Density of Stochastic Differential Equations with Stochastic Calculus of Standard Deviations

<t>Hello Amin,It might be good marketing to periodically post your updates, but frankly, this is a lot of stuff to read and a good deal of it is rather cryptic (moreover, the paper you cited in the beginning is already three years old and does not contain your updates, I guess). So, as I'm also head...
March 11th, 2015, 7:39 pm
Forum: Technical Forum
Topic: Equivalence of Closed-Form Density and Eigenfunction Representation of Density
Replies: 9
Views: 3743

### Equivalence of Closed-Form Density and Eigenfunction Representation of Density

<t>QuoteOriginally posted by: OrbitActually my original thought was that my solution would already be an eigenfunction expansion.Mine as well. You have two ingredients here: the closed function $p(x)$ and some solution $g(x)$ in terms of eigenfunctions (--or any other complete orthonormal ba...
March 11th, 2015, 2:52 pm
Forum: Technical Forum
Topic: Equivalence of Closed-Form Density and Eigenfunction Representation of Density
Replies: 9
Views: 3743

### Equivalence of Closed-Form Density and Eigenfunction Representation of Density

<t>Another simple way is to expand your solution (log-normal or whatever) into the basis of eigenfunctions. If all such obtained expansions coefficients are identical to the ones you have in your series, there you go.This is so to say the other direction of Alan's alternative number 4 (--or, in othe...
March 8th, 2015, 1:20 pm
Topic: Trading with pricing models
Replies: 9
Views: 5452

### Trading with pricing models

<r>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 corres...
March 5th, 2015, 8:04 pm
Topic: Trading with pricing models
Replies: 9
Views: 5452

### Trading with pricing models

<r>QuoteOriginally posted by: AlanBecome a market maker at the CBOE.This is anyways the next plan. Do you have any other ideas? :-)QuoteOriginally posted by: savrTell me what your model describes, and perhaps someone can tell you how to use it.I was talking about a solver for stochastic models. Let'...
March 5th, 2015, 1:12 pm
Forum: Numerical Methods Forum
Topic: Spectral Decomposition
Replies: 9
Views: 4026

### Spectral Decomposition

<r>Can you estimate in detail the advantages which you're looking for by using a spectral decomposition? When it's "only" about PDE-propagation, it's maybe not that easy to definitely state the advantages over the short-time propagation methods: the spectral method takes O(N^3) once for the decompos...
March 5th, 2015, 11:57 am
Forum: Numerical Methods Forum
Topic: Is HJB equation a local or global optimum?
Replies: 1
Views: 4672

### Is HJB equation a local or global optimum?

<t>The funny thing here is that you scratch your head only as you forgot the assumptions. You are completely right, a sequence of local optima doesn't make up to the global optimum. If it were like this optimization theory would be complete at the level of greedy functions.However, the HJB (or its d...
March 5th, 2015, 11:23 am
Forum: Numerical Methods Forum
Topic: Spectral Decomposition
Replies: 9
Views: 4026

### Spectral Decomposition

<t>The usual solution when you have time-dependent functions is to use the decomposition only for a short-time propagation. The idea is this: if you want to evolve your equation (--let's assume time-independent coefficient functions for the first) to arbitrarily long times, you need all eigenvectors...
March 5th, 2015, 9:43 am
Topic: Trading with pricing models
Replies: 9
Views: 5452

### Trading with pricing models

<t>This is probably some old stuff for some, but it is a question which I couldn't definitely answer by myself in the last two years, so your comments are welcome.Derivatives of any kind are usually described via stochastic models and managed in practice by standard Monte Carlo and PDE methods (my b...
March 5th, 2015, 9:24 am