Erlang risk models and finite time ruin problems

Abstract

We consider the joint density of the time of ruin and deficit at ruin in the Erlang(n) risk model. We give a general formula for this joint density and illustrate how the components of this formula can be found in the special case when n=2. We then show how the formula can be implemented numerically for a general value of n. We also discuss how the ideas extend to the generalised Erlang(n) risk model. © 2012 Copyright Taylor and Francis Group, LLC.