Ergodicity Breaking in Geometric Brownian Motion
Abstract
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this Letter, we study the effects of diversification using the concept of ergodicity breaking.
- Publication:
-
Physical Review Letters
- Pub Date:
- March 2013
- DOI:
- 10.1103/PhysRevLett.110.100603
- arXiv:
- arXiv:1209.4517
- Bibcode:
- 2013PhRvL.110j0603P
- Keywords:
-
- 05.40.Jc;
- 02.50.Ey;
- 05.10.Gg;
- 05.20.Gg;
- Brownian motion;
- Stochastic processes;
- Stochastic analysis methods;
- Classical ensemble theory;
- Mathematical Physics;
- Quantitative Finance - Risk Management
- E-Print:
- 5 pages, 3 figures