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theRedBaron
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Abstract Algebra(applications)

December 26th, 2010, 12:43 pm

I was wondering if you guys have any ideas on applying abstract algebra in finance and trading? Perhaps there's some resource you can recommend?
 
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frenchX
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Abstract Algebra(applications)

December 26th, 2010, 1:59 pm

As the name implies "abstract algebra" is quite abstract I remember a few group theory applications could be use but mainly in research.Group theory could be use for Lévy process. The same that for HAM (homotopy analysis method) for american options.
 
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tags
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Abstract Algebra(applications)

December 26th, 2010, 2:09 pm

there are (at least) two previous threads on wilmott discussing on abstract algebraone got people frustrated : http://www.wilmott.com/messageview.cfm? ... E=1another one proposes some (but few ) tracks to follow : http://www.wilmott.com/messageview.cfm? ... TARTPAGE=1
Last edited by tags on December 25th, 2010, 11:00 pm, edited 1 time in total.
 
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Cuchulainn
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Abstract Algebra(applications)

December 26th, 2010, 3:43 pm

QuoteOriginally posted by: edouardthere are (at least) two previous threads on wilmott discussing on abstract algebraone got people frustrated : http://www.wilmott.com/messageview.cfm? ... E=1another one proposes some but few : tracks to follow : http://www.wilmott.com/messageview.cfm? ... TARTPAGE=1
Last edited by Cuchulainn on December 25th, 2010, 11:00 pm, edited 1 time in total.
 
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frenchX
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Abstract Algebra(applications)

December 26th, 2010, 4:12 pm

Abstract algebra can be beautiful But I agree that it's hardly appliable in finance Abstract algebra is a bit abstract for me but for example I truly believe in other maths domain as Malliavin calculus, nonlinear stochastic dynamics and why not multidimensional random walks or fractal chaos. If you were a physicist I would say that abstract algebra is usefull (especially in quantum mechanics or relativistic QCD) but in finance ...
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Alan
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Abstract Algebra(applications)

December 26th, 2010, 5:31 pm

There was an interesting paper a few years back, using Lie algebra tosolve the time-dependent CEV model:http://papers.ssrn.com/sol3/papers.cfm? ... d=984373It is somewhat overkill, as the problem can be solved directly, but I thinkthe authors may have still been the first to get the soln. Also, the OP may be interested in the classification of solvable models, as inH-Labordere's http://arxiv.org/PS_cache/cond-mat/pdf/ ... 1028v1.pdf Or, just did a little googling and turned up this kind of thing: http://www.math.umn.edu/conferences/s4/ ... .pdf,which again speaks to exactly solvable (diffusion) problems by changing i d/dt of QM to d/dtand so just replace Schrodinger in title slide by "Kolmogorov"
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Cuchulainn
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Abstract Algebra(applications)

December 27th, 2010, 3:16 pm

Related to the Lie algebra approach..A few years ago here there was a _lot_of talk about BCH In some sense it includes ADI and Soviet Splitting methods. Quotehttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=984373Equation (36) is a nightmareI have still to see a computable solution tou_t = au_xx + bu_x using Lie theory. Heat eq, kdv, sine Gordon yes but these seem to be easy for some reason.
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Alan
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Abstract Algebra(applications)

December 27th, 2010, 4:29 pm

QuoteOriginally posted by: CuchulainnRelated to the Lie algebra approach..Quotehttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=984373Equation (36) is a nightmareNot really, it's just eqn (1) here without the abbrevs:http://portal.tugraz.at/portal/page/por ... r_1989.pdf
 
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Cuchulainn
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Abstract Algebra(applications)

December 27th, 2010, 4:47 pm

QuoteOriginally posted by: AlanQuoteOriginally posted by: CuchulainnRelated to the Lie algebra approach..Quotehttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=984373Equation (36) is a nightmareNot really, it's just eqn (1) here without the abbrevs:http://portal.tugraz.at/portal/page/por ... 1989.pdfAh, just modified Bessels and Noncentral chi^2. Piece of cake
 
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frenchX
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Abstract Algebra(applications)

December 27th, 2010, 5:37 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: AlanQuoteOriginally posted by: CuchulainnRelated to the Lie algebra approach..Quotehttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=984373Equation (36) is a nightmareNot really, it's just eqn (1) here without the abbrevs:http://portal.tugraz.at/portal/page/por ... 1989.pdfAh, just modified Bessels and Noncentral chi^2. Piece of cakeModified Bessel are painfull ( I use them for plasmon dispersion relation). The book of Abramovich is your friend
 
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Cuchulainn
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Abstract Algebra(applications)

December 27th, 2010, 6:06 pm

QuoteModified Bessel are painfull ( I use them for plasmon dispersion relation). The book of Abramovich and Stegun is your friend It's so easy now Bessel Bessel, the Maths Thanks to the great work by the Math Toolkit builders.
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AVt
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Abstract Algebra(applications)

December 27th, 2010, 8:47 pm

I did abstract algebra (what ever that may be .. finally enjoyed derived categories and its applications).A cynical reply: why do you expect abstract Math/Physics/... provides answers for concrete problems?A practical advice: do not try to find applications for theoretical approaches (except for fund raising),if starting then the other way round is not the worst.If being interested in algebra, then it is fine (and a *long* route). But if applications are your desire,then avoid it like the plague.
 
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Costeanu
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Abstract Algebra(applications)

December 27th, 2010, 11:26 pm

At the end of Labordere's book there is a chapter with applications of Hopf algebras to finding local volatility models that can be exactly (weakly) simulated. Regarding applications of category theory to math fin, I'm not aware of a direct application. However, they are used in functional programming, like Haskell. And I remember seeing an article about applications of "combinators" (from Haskell) to pricing of generic financial derivatives.