Showing papers by "Barbara Martinucci published in 2019"
TL;DR: A wide generalization of known results related to the telegraph process on a straight line and their generalizations on an arbitrary state space are proposed.
Abstract: We propose a wide generalization of known results related to the telegraph process. Functionals of the simple telegraph process on a straight line and their generalizations on an arbitrary state space are studied.
8 citations
TL;DR: In this article, the authors consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice and determine the probability generating functions, the transition probabilities and the relevant moments.
Abstract: We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.
4 citations
TL;DR: In this paper, the jump telegraph process was considered and the incomplete financial market model based on this process was studied, which can price switching risks as well as jump risks of the model.
Abstract: We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.
3 citations