On Prices' evolutions based on geometric telegrapher's process

The geometric telegrapher’s process is proposed as a model to describe the dynamics of the price of risky assets. When the underlying random inter-times have Erlang distribution we express the probability law of such process in terms of a suitable two-index pseudo-Bessel function. Stochastic comparisons of two geometric telegrapher’s processes based on the usual stochastic order (FSD comparison) and on the stop-loss order are also performed. Various examples of application of such comparisons are then provided