Large systems of diffusions interacting through their ranks

Mykhaylo Shkolnikov

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1730-1747

Abstract: We study the limiting behavior of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that under certain assumptions the limiting dynamics is given by a McKean–Vlasov evolution equation. Moreover, we show that the evolution of the cumulative distribution function under the limiting dynamics is governed by the generalized porous medium equation with convection. The implications of the results for rank-based models of capital distributions in financial markets are also explained.

Keywords: Diffusion processes; McKean–Vlasov equation; Porous medium equation; Particle method; Capital distributions; Rank-based market models (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:4:p:1730-1747

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DOI: 10.1016/j.spa.2012.01.011

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