IJPAM: Volume 106, No. 1 (2016)

ON THE GERBER-SHIU PENALTY FUNCTION FOR
THE COMPOUND BINOMIAL RISK MODEL
WITH DELAYED CLAIMS

Zhenhua Bao$^1$, He Liu$^2$, Ye Liu$^3$
$^{1,3}$School of Mathematics
Liaoning Normal University
Dalian, 116029, P.R. CHINA
$^2$School of Mathematics,
Physics and Biological Engineering
Inner Mongolia University of Science and Technology
Baotou, 014010, P.R. CHINA


Abstract. In this paper we consider the Gerber-Shiu penalty function in the compound binomial risk model with time-correlated claims. It is assumed that each main claim will induce a by-claim but the occurrence of the by-claim may be delayed with a certain probability. Formulas for the probability generating function of the penalty function are obtained, together with the expression for the penalty function with zero initial surplus. Then we show that the penalty function satisfies a defective renewal equation. When the claims follow geometric distributions, explicit expression for the Gerber-Shiu function is derived. Numerical example is provided to illustrate the application of the result discussed in the paper.

Received: August 28, 2015

AMS Subject Classification: 62P05, 91B30

Key Words and Phrases: main claim, by-claim, probability generating function, Gerber-shiu function, defective renewal equation

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DOI: 10.12732/ijpam.v106i1.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 127 - 140


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