IJPAM: Volume 82, No. 3 (2013)
WITH STOCHASTIC INCOME
School of Mathematics
Liaoning Normal University
Dalian, 116029, P.R. CHINA
Abstract. In this paper we consider a risk model where both premiums and claims follow compound binomial processes. A difference equation and a defective renewal equation satisfied respectively by the expected discounted penalty function are derived. Then for a special penalty function and geometrically distributed claim amounts, an explicit expression of the expected discounted penalty function is obtained. Finally, we investigate the case when premiums are degenerate at a constant amount. We derive an alternative defective renewal equation in terms of the roots of the generalized Lundberg's fundamental equation.
Received: July 26, 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