The Annals of Applied Probability

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.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 3 (2011), 1180-1213.

Dates
First available in Project Euclid: 2 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1307020395

Digital Object Identifier
doi:10.1214/10-AAP725

Mathematical Reviews number (MathSciNet)
MR2830616

Zentralblatt MATH identifier
1225.60136

Subjects
Primary: 60J60: Diffusion processes [See also 58J65] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 91B28

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

Citation

Pal, Soumik. Analysis of market weights under volatility-stabilized market models. Ann. Appl. Probab. 21 (2011), no. 3, 1180--1213. doi:10.1214/10-AAP725. https://projecteuclid.org/euclid.aoap/1307020395


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