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I am looking for papers that would describe asset allocation with geometry, group theory, markov chains or things like that. Keeping asset allocation in a range is easy but to keep it more precisely is harder. I find it often hard to judge things such as evaluation of trading costs and cause-effect -relationship (particularly when the relationships are long).

Here are some phases or states which I would like to control better:

  • Cash is liquid which can change to any other asset with 2 phase: holding cash and buy another asset.
  • The change of a fund requires that you sell it first to cash and then to your indented fund -- 3 phase.
  • Changing fund to the better, 3phase but too expensive better to keep the old.
  • much more phases!

Reference material appreciated.

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2 Answers

Here example of practical application of Markov ideas to trading.

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+1 very clever to use Forex and the conditional prob with markov chains. There must be more into this issue. –  hhh Jul 23 '11 at 21:14
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I think you might be interested by an article I mentioned in this post:

Carlo Acerbi from MSCI presents in this presentation an innovative approach to liquidity risk. The idea is basically to model how liquid an asset is and how your portfolio allocation should take this risk into account.

This way of seeing risk is in my opinion pretty interesting an quite brilliant.

Hopefully, it'll be the kind of theory you're looking for.

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SRKX: did you read 12 and 14? The sum of two diff assets is in general "undefined" but still the author creates a portfolio defined by a vector under scalar multiplication and addition. Now what I need is more "granuality": allocations are groups A->B->C->D->A. If A increases, it forms a chain of actions until hitting A again. Now you can have chains of different length X->C->Y-X. Suppose Y increases, it pushes the last chain changing the Intedented first chain to A->B->X->D->A. Now the key is between actual and intended chains which differ for sure. Now portfolio is not vector but groups. –  hhh Jul 18 '11 at 19:19
    
@hhh: not sure if you mean the tone of your comment... if you do, I seriously regret even taking the time to find back the presentation and posting the answer. As for the rest of the comment, I'd suggest you include it back in the question for clarity purpose. As for Acerbi's presentation, what I understood is that indeed you cannot price the asset as a collection and he attempts to find some other way to come up with a price. I don't remember all the details, I was trying to give a clue. –  SRKX Jul 18 '11 at 21:52
    
SRKX: now I got a bit lost by your comment myself. I am trying to find out whether there exist some paper that would model portfolio more quantifially. For example, by the "group theory" I am looking for whether someone has modelled differed allocations in groups. Allocation "fixed income" would form a group which act different to different allocations such as "US market". The paper simplifies portfolio to a vector but I would like to visualize actions between different allocations, I cannot see such simplification would allow me to do it. Question contain some phases to model, for example. –  hhh Jul 19 '11 at 5:56
    
Today such models are usually just done with statistics, calculate the covariance matrix between different assets or allocations -- fine, works. Now, I am interested to know deeper details -- to model how things act under the roof, I know there may be no general theory but I am still interested whether someone has gone a step further in quantifying allocating. The phases could easily form a markov chain, in the question. Allocation types could be different groups. You can probably understand the paper better, does it help in quantifying a step further? –  hhh Jul 19 '11 at 5:58
    
you should include the comments in the question, maybe someone esle can help. –  SRKX Jul 19 '11 at 6:54
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