A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations...

In this paper we overcome a lacks of Black-Scholes model, i.e. the infinite propagation velocity, the infinitely large asset prices etc. The proposed model is based on the telegraph process with jumps. The option price formula is derived.

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

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and jumps, which occur with velocity switches. Given that jump directions match velocity directions of the underlying random motion properly in relation to interest...

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and jumps, which occur with velocity switches. Given that jump directions match velocity directions of the underlying random motion properly in relation to interest...

The paper develops a class of Financial market models with jumps based on a Brownian motion, and inhomogeneous telegraph processes: random motions with alternating velocities. We assume that jumps occur when the velocities are switching. The distribution of such a process is described in detail....

The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under...

The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are switching. We argue that such a model captures well the stock...

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and jumps occurring when the velocities are switching. This model is free of arbitrage if jump directions are in a certain correspondence with the velocities of the...

For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in...