A Duality Result for the Generalized Erlang Risk Model

Abstract

In this article, we consider the generalized Erlang risk model and its dual model. By using a conditional measure-preserving correspondence between the two models, we derive an identity for two interesting conditional probabilities. Applications to the discounted joint density of the surplus prior to ruin and the deficit at ruin are also discussed.

Keywords

• generalized Erlang risk model
• duality
• conditional measure-preservation
• the Lundberg fundamental equation
• joint density
• surplus prior to ruin
• deficit at ruin