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EnglishA basic model in mathematical finance theory is the celebrated geometric Brownian motion. Moreover, the geometric telegraph process is a simpler model to describe the alternating dynamics of the price of risky assets. In this note we consider a more general stochastic process that combines the characteristics of such two models. Precisely, we deal with a geometric Brownian motion with alternating trend. It is defined as the exponential of a standard Brownian motion whose drift alternates randomly between a positive and a negative value according to a generalized telegraph process. We express the probability law of this process as a suitable mixture of Gaussian densities, where the weighting measure is the probability law of the occupation time of the underlying telegraph process.
| Titolo: | On the geometric Brownian motion with alternating trend | |
| Autori: | ||
| Data di pubblicazione: | 2014 | |
| Handle: | http://hdl.handle.net/11386/4520657 | |
| ISBN: | 9783319050133 9783319050140 | |
| Appare nelle tipologie: | 2.1.2 Articolo su libro con ISBN |
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