Large volatility-stabilized markets

2011/02/17 by Mykhaylo Shkolnikov, Shkolnikov, Mykhaylo · 1 citation
Economics, Econometrics and Finance · #91G80 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 60J60 #Probability (math.PR) #Stochastic processes and financial applications #secondary 60J70

paper · pdf · doi:10.48550/arxiv.1102.3461

openalex publication_date 2011/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an appropriate rescaling of the time parameter, the empirical measure of the system converges to the solution of a degenerate parabolic partial differential equation. A stochastic representation of the latter in terms of one-dimensional distributions of a time-changed squared Bessel process allows us to give an explicit description of the limit.

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