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ON BOUNCING GEOMETRIC BROWNIAN MOTIONS
Published online by Cambridge University Press: 27 December 2018
Abstract
A pair of bouncing geometric Brownian motions (GBMs) is studied. The bouncing GBMs behave like GBMs except that, when they meet, they bounce off away from each other. The object of interest is the position process, which is defined as the position of the latest meeting point at each time. We study the distributions of the time and position of their meeting points, and show that the suitably scaled logarithmic position process converges weakly to a standard Brownian motion as the bounce size δ→0. We also establish the convergence of the bouncing GBMs to mutually reflected GBMs as δ→0. Finally, applying our model to limit order books, we derive a simple and effective prediction formula for trading prices.
Keywords
- Type
- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 33 , Issue 4 , October 2019 , pp. 591 - 617
- Copyright
- Copyright © Cambridge University Press 2018