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• W3121323323 abstract "We consider systems of diffusion processes (“particles”) interacting through their ranks (also referred to as “rank-based models” in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to the solution of a linear parabolic SPDE with additive noise. The coefficients in the limiting SPDE are determined by the hydrodynamic limit of the particle system which, in turn, can be described by the porous medium PDE. The result opens the door to a thorough investigation of large equity markets and investment therein. In the course of the proof, we also derive quantitative propagation of chaos estimates for the particle system." @default.
• W3121323323 created "2021-02-01" @default.
• W3121323323 creator A5009434022 @default.
• W3121323323 creator A5081893217 @default.
• W3121323323 date "2018-03-01" @default.
• W3121323323 modified "2023-10-13" @default.
• W3121323323 title "SPDE limit of the global fluctuations in rank-based models" @default.
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• W3121323323 doi "https://doi.org/10.1214/17-aop1200" @default.
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