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

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.

Keywords

Gerber-Shiu function / phase-type distribution / Dickson-Hipp operator

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