The Gerber-Shiu expected penalty function for the risk model with dependence and a constant dividend barrier. (English) Zbl 1406.91201

Liu, Donghai; Liu, Zaiming; Peng, Dan

Abstr. Appl. Anal. 2014, Article ID 730174, 7 p. (2014).

Summary: We consider a compound Poisson risk model with dependence and a constant dividend barrier. A dependence structure between the claim amount and the interclaim time is introduced through a Farlie-Gumbel-Morgenstern copula. An integrodifferential equation for the Gerber-Shiu discounted penalty function is derived. We also solve the integrodifferential equation and show that the solution is a linear combination of the Gerber-Shiu function with no barrier and the solution of an associated homogeneous integrodifferential equation.

MSC:

91B30	Risk theory, insurance (MSC2010)
60K10	Applications of renewal theory (reliability, demand theory, etc.)
45J05	Integro-ordinary differential equations

Keywords:

Gerber-Shiu discounted penalty function; risk model; constant dividend barrier

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