Large volatility-stabilized markets

Details Large volatility-stabilized markets Large volatility-stabilized markets

2011-02-17

arxiv.org/abs/1102.3461v1

Mathematics

Probability

17 pages

Scientific paper

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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