Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 3: 437 - 448

DOI: https://doi.org/10.1007/s11464-012-0176-7

RESEARCH ARTICLE

A matrix operator approach to a risk model with two classes of claims

  • Hua DONG , 1 ,
  • Zaiming LIU 2
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  • 1. School of Mathematics, Qufu Normal University, Qufu 273165, China
  • 2. School of Mathematics, Central South University, Changsha 410075, China

Received date: 20 Dec 2010

Accepted date: 09 Nov 2011

Published date: 01 Jun 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

In this paper, we study a risk model with two independent classes of risks, in which both claim number processes are renewal processes with phasetype inter-arrival times. Using a generalized matrix Dickson-Hipp operator, a matrix Volterra integral equation for the Gerber-Shiu function is derived. And the analytical solution to the Gerber-Shiu function is also provided.

Key words： Gerber-Shiu function; phase-type distribution; Dickson-Hipp operator

Cite this article

Hua DONG , Zaiming LIU . A matrix operator approach to a risk model with two classes of claims[J]. Frontiers of Mathematics in China, 2012 , 7(3) : 437 -448 . DOI: 10.1007/s11464-012-0176-7

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