Escape probabilities of compound renewal processes with drift
Probability
2019-07-30 v1
Abstract
We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only negative jumps arise we give a general solution for escape and survival probabilities under Erlang and hypo-exponential arrivals. These ideas are generalized to the class of arrival distributions having rational Laplace transforms. In a general situation with two-sided jumps we also identify important families of solvable cases. A parallelism with the "scale function" of diffusion processes is drawn.
Keywords
Cite
@article{arxiv.1907.11894,
title = {Escape probabilities of compound renewal processes with drift},
author = {Javier Villarroel and Juan A. Vega and Miquel Montero},
journal= {arXiv preprint arXiv:1907.11894},
year = {2019}
}