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The model given in the following paper by Avellaneda et al

http://people.stern.nyu.edu/jreed/Papers/limitorder.pdf

On page 7 he explains that the initial Bid and Ask size should be normalised by their median size. This leads to equation 3.8 on p10.

The same equation was also derived by Cont and de LARRARD eqn 36 p30

http://arxiv.org/pdf/1202.6412v1.pdf

However when he normalises the initial Bid and Ask sizes he uses the sqrt of n see eqn 12 on p20?

How are these normalisations equivalent? They seem quite different yet lead to the same solution?

More confusingly when Avellaneda et al calculate the analytical probs on p14 only the decile values are used (e.g 0.1) which is different again from the two normalisations mentioned above?

Q1. Are the three normalisations equivalent?

Lastly what is the correct interpretation of the eqn shown in Proposition 2 on p27 of Cont and de LARRARD?

Q2.) Are the Bessel functions of the first or second kind? (First I think).

Q3.) Is the infinite sum shown an example of an infinite Bessel series?

If the answer to Q3 is yes can these be evaluated numerically for example in Matlab?

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