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SOME ADVANCES ON THE ERLANG(n) DUAL RISK MODEL

Published online by Cambridge University Press:  27 August 2014

Eugenio V. Rodríguez-Martínez ,
Rui M. R. Cardoso  and
Alfredo D. Egídio dos Reis
Eugenio V. Rodríguez-Martínez
Affiliation:
ISEG and CEMAPRE, Department of Mathematics, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal E-Mail: evrodriguez@gmail.com
Rui M. R. Cardoso
Affiliation:
Centro de Matemática e Aplicações, Department of Mathematics, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte de Caparica, 2829-516 Caparica, Portugal E-Mail: rrc@fct.unl.pt
Alfredo D. Egídio dos Reis*
Affiliation:
ISEG and CEMAPRE, Department of Management, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal
*
E-Mail: alfredo@iseg.utl.pt
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Abstract

The dual risk model assumes that the surplus of a company decreases at a constant rate over time and grows by means of upward jumps, which occur at random times and sizes. It is said to have applications to companies with economical activities involved in research and development. This model is dual to the well-known Cramér-Lundberg risk model with applications to insurance. Most existing results on the study of the dual model assume that the random waiting times between consecutive gains follow an exponential distribution, as in the classical Cramér-Lundberg risk model. We generalize to other compound renewal risk models where such waiting times are Erlang(n) distributed. Using the roots of the fundamental and the generalized Lundberg's equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Furthermore, we compute expected discounted dividends, as well as higher moments, when the individual common gains follow a Phase-Type, PH(m), distribution. We also perform illustrations working some examples for some particular gain distributions and obtain numerical results.

Keywords

Dual risk modelErlang(n) interarrival timesPhase-Type distributiongeneralized Lundberg's equationruin probabilitytime of ruinexpected discounted dividends
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 1 , January 2015 , pp. 127 - 150
Copyright
Copyright © ASTIN Bulletin 2014 

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