The maximum surplus before ruin in an Erlang(n) risk process and related problems [An article from: Insurance Mathematics and Economics]

This digital document is a journal article from Insurance Mathematics and Economics, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
We study the distribution of the maximum surplus before ruin in a Sparre Andersen risk process with the inter-claim times being Erlang(n) distributed. This distribution can be analyzed through the probability that the surplus process attains a given level from the initial surplus without first falling below zero. This probability, viewed as a function of the initial surplus and the given level, satisfies a homogeneous integro-differential equation with certain boundary conditions. Its solution can be expressed as a linear combination of n linearly independent particular solutions of the homogeneous integro-differential equation. Explicit results are obtained when the individual claim amounts are rationally distributed. When n=2, all the results can be expressed explicitly in terms of the non-ruin probability. We apply our results by looking at (i) the maximum severity of ruin and (ii) the distribution of the amount of dividends under a constant dividend barrier.