Exact Distribution of Verhulst process

Maciej Wiśniewolski; Jacek Jakubowski

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arXiv · 1408.6727

Exact Distribution of Verhulst process

Maciej Wiśniewolski·Jacek Jakubowski

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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.

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BibTeX RIS

Maciej Wiśniewolski, Jacek Jakubowski. 2014-08-28. Exact Distribution of Verhulst process. https://arxiv.org/abs/1408.6727

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