A Duality Result for the Generalized Erlang Risk Model

Risks

Lanpeng Ji²  Chunsheng Zhang¹ 

[1] School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China; E-Mail:;Department of Actuarial Science, University of Lausanne, Bâtiment Extranef, UNIL-Dorigny, 1015 Lausanne, Switzerland

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

DOI  :  10.3390/risks2040456

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.