Analysis of the market weights under the Volatility-Stabilized Market models

Details Analysis of the market weights under the Volatility-Stabilized Market models Analysis of the market weights under the Volatility-Stabilized Market models

2009-04-03

arxiv.org/abs/0904.0656v3

Mathematics

Probability

38 pages

Scientific paper

We derive the joint density of market weights, at fixed times and suitable stopping times, of the Volatility-stabilized market models introduced by Fernholz and Karatzas in 2005. The argument rests on computing the exit density of a collection of independent Bessel-square processes of possibly different dimensions from the unit simplex. We show that the law of the market weights is the same as that of the multi-allele Wright-Fisher diffusion model, well-known in population genetics. Thus, as a side result we furnish a novel proof of the transition density function of the Wright-Fisher model which was originally derived by Griffiths by bi-orthogonal series expansion.

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