Exact Distribution of Verhulst process
Probability
2014-08-29 v1
Abstract
We investigate a Verhulst process, which is the special functional of geometric Brownian motion and has many applications, among others in biology and in stochastic volatility models. We present an exact form of density of a one dimensional distribution of Verhulst process. Simple formula for the density of Verhulst process is obtained in the special case, when the drift of geometric Brownian motion is equal to -1/2. Some special properties of this process are discussed, e.g. it turns out that under Girsanov's change of measure a Verhulst process still remains a Verhulst process but with different parameters.
Keywords
Cite
@article{arxiv.1408.6727,
title = {Exact Distribution of Verhulst process},
author = {Maciej Wiśniewolski and Jacek Jakubowski},
journal= {arXiv preprint arXiv:1408.6727},
year = {2014}
}
Comments
11 pages