Escape probabilities of compound renewal processes with drift

Javier Villarroel; Juan A. Vega; Miquel Montero

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arXiv · 1907.11894

Escape probabilities of compound renewal processes with drift

Javier Villarroel·Juan A. Vega·Miquel Montero

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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$(n)$ 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.

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Javier Villarroel, Juan A. Vega, Miquel Montero. 2019-07-27. Escape probabilities of compound renewal processes with drift. https://arxiv.org/abs/1907.11894

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