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June 2011 Analysis of market weights under volatility-stabilized market models
Soumik Pal
Ann. Appl. Probab. 21(3): 1180-1213 (June 2011). DOI: 10.1214/10-AAP725

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. "Analysis of market weights under volatility-stabilized market models." Ann. Appl. Probab. 21 (3) 1180 - 1213, June 2011. https://doi.org/10.1214/10-AAP725

Information

Published: June 2011
First available in Project Euclid: 2 June 2011

zbMATH: 1225.60136
MathSciNet: MR2830616
Digital Object Identifier: 10.1214/10-AAP725

Subjects:
Primary: 60J35 , 60J60 , 60J70 , 91B28

Keywords: Bessel processes , Kelvin transform , market weights , Volatility-stabilized markets , Wright–Fisher model

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 3 • June 2011
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