Abstract
The geometric telegrapher’s process has been proposed in 2002 as a model to describe the dynamics of the price of risky assets. In this contribution we consider a related stochastic process, whose trajectories have two alternating slopes, for which the random times between consecutive slope changes have exponential distribution with linearly increasing parameters. This leads to a process characterized by a damped behavior. We study the main features of the transient probability law of the process, and of its stationary limit.
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Acknowledgements
The research of Antonio Di Crescenzo and Barbara Martinucci has been performed under partial support by MIUR (PRIN 2008).
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Di Crescenzo, A., Martinucci, B., Zacks, S. (2012). On the damped geometric telegrapher’s process. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-2342-0_21
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DOI: https://doi.org/10.1007/978-88-470-2342-0_21
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2341-3
Online ISBN: 978-88-470-2342-0
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