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arXiv · 0904.0656

Analysis of market weights under volatility-stabilized market models

Soumik Pal
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Abstract

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 [Ann. Finan. 1 (2005) 149-177]. 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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Soumik Pal. 2009-04-03. Analysis of market weights under volatility-stabilized market models. https://doi.org/10.1214/10-aap725

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