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### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 11th, 2011, 6:47 pm**

by **frenchX**

The quickest algos for optilization are the one based on differential evolution. Computer science lab which wants to win the IEEE optimization contest only use variant of this algo.

### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 11th, 2011, 6:53 pm**

by **Alan**

QuoteOriginally posted by: outrunYes please share ideas regarding interior point methods, I've ran into it only a bit -a long time ago- with EM performance papers, and with stochastic dispatch optimization of groups of powerplants.another design element is that for some problems we can faster calculate the 200 option prices "as a set", than 200 times and individual option, e.g. with forward methods.I'll have to think about this, how can we generalize elements of the steps involved into modules, and be flexible enough to slip in performance boosting hints.Sure, here's the implementation notes I refer to. (scroll to 'The Interior Point Algorithm')Regarding forward methods, agree: I am implicitly assuming they will be used, so that all the options at a given expiration are handled as efficiently as possible.The Fang-Oosterlee method is a nice example of that.

### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 11th, 2011, 11:29 pm**

by **Alan**

QuoteOriginally posted by: outrunQuoteSearching for Fang-Oosterlee, I found out that Oosterlee works around the corner You're referring to COS inversion method, right?Great, you can ask him questions. Yes, the COS method -- the main advantage for calibration is that it is a vectorized method; you can pass ita vector of N strikes for a given expiration. It requires a vector of char. function values at M points, and then you get a vectorof option prices at those strikes from OptionVec = mat . CharFuncVec, where mat is a very simple N x M matrix. So, if the char. function is obtainedfrom a call to Daniel's pde routine, there are only M calls to that, regardless of the number of options with that fixed expiration.So it minimizes the number of calls to the most computationally expensive function, which is the char. function.

### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 12th, 2011, 5:32 am**

by **frenchX**

QuoteOriginally posted by: outrunQuoteOriginally posted by: frenchXThe quickest algos for optilization are the one based on differential evolution. Computer science lab which wants to win the IEEE optimization contest only use variant of this algo.can you give some links? option prices have gradients pointing is similar directions, that might be something that can be utilized as wellYes here is a link

http://www.wilmott.com/messageview.cfm? ... adid=86944

### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 12th, 2011, 10:15 pm**

by **Alan**

Yes. When I call FindMinimum[...] in Mathematica, I just give it an objective function and constraints -- that's it (apart from convergence criteria, step monitoring options, etc.).If the objective function is very simple, I think Mathematica will attempt to get symbolic derivatives. Failing that, which indeed fails for these calibration type problems, the routine must do numerical derivatives.

### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 13th, 2011, 7:38 pm**

by **Cuchulainn**

For the FD framework I am planning to use uBLAS (and multiarray) as storage and boost function for all PDE/FDM functions. I will customise the engines by allowing events to be non-intrusively be added to the running engine. (signals2)What do you think?

### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 13th, 2011, 7:44 pm**

by **Polter**

Regarding uBLAS -- I've made a post before. BTW, have you considered dlib?Regarding signals -- some of the points to investigate:

http://www.gotw.ca/gotw/083.htmhttp://e ... alandslots

### PDE/PIDE (FDM. FEM) methods thread

Posted: **October 15th, 2011, 10:59 am**

by **Cuchulainn**

QuoteI would suggest to try and isolate generic algorithms bits (like std::sort with compare is) and make the engine more like a template lib instead of a program. Is that your plan?It is a traditional OO framework at the moment, so the new one will be similar. It is at level 2 and it is difficult to see how it will useful as a library because of the nature of the problem. I do see level modules being needed, however.Maybe it is possible to do it like a template: FDM<Pde, Domain, Mesher, FDMAlgo, Matrix, Output> ?? Each param corresponding to one 'business' concern or attention area. I could provide both options..