Ergodicity breaking in geometric Brownian motion
Mathematical Physics
2013-03-15 v3 math.MP
Risk Management
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 non-ergodicity, 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.
Cite
@article{arxiv.1209.4517,
title = {Ergodicity breaking in geometric Brownian motion},
author = {Ole Peters and William Klein},
journal= {arXiv preprint arXiv:1209.4517},
year = {2013}
}
Comments
5 pages, 3 figures