Large volatility-stabilized markets

Research output: Contribution to journalArticle

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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.

Original languageEnglish (US)
Pages (from-to)212-228
Number of pages17
JournalStochastic Processes and their Applications
Volume123
Issue number1
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Bessel processes
  • Degenerate parabolic partial differential equations
  • Hydrodynamic limit
  • Interacting diffusion processes
  • Volatility-stabilized models

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