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 introduce 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 correspondence with the velocity directions of the underlying random motion...

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...