IJPAM: Volume 79, No. 2 (2012)

ON THE DISCOUNTED FACTORIAL MOMENTS OF
THE DEFICIT IN THE DISCRETE TIME
RENEWAL RISK MODEL

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


Abstract. In this paper we consider a discrete time renewal risk model with arbitrary interclaim times. An explicit formula is derived for the discounted factorial moments of the deficit at ruin by using a recursive equation satisfied by the Gerber-Shiu discounted penalty function. Numerical illustrations are also given to show that the formula obtained is readily programmable and works well for special claim distributions.

Received: June 14, 2012

AMS Subject Classification: 62P05, 91B30

Key Words and Phrases: compound binomial model, defective renewal equation, difference equation, expected discounted penalty function

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 2