In this paper we develop a financial market model based on continuous time random motions with alternating constant velocities and with jumps occurring when the velocity switches. If jump directions are in the certain ...

The paper develops a class of financial market models with jumps based on aBrownian motion, and inhomogeneous telegraph processes: random motions withalternating velocities. We assume that jumps occur when the velocities ...

The traditional jump-telegraph processes are based on a Poisson process with alternating intensities. We develop a new model based on an alternating doubly stochastic Poisson process with random intensities of jumps. ...

We study the long-time behavior of variants of the telegraph process with position-dependent jump rates, which result in a monotone gradient-like drift towards the origin. We compute their invariant laws and obtain, via ...

We continue to study financial market models based on generalized telegraph processes with alternating velocities. The model is supplied with jumps occurring at the times of velocity switchings. This model is arbitrage-free ...

We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state ...

The paper presents exact formulae related to the distribution of the first passage time ?x of the jump-telegraph process. In particular, the Laplace transform of ?x is analysed, when a jump component is in the opposite ...