Gerber-Shiu Function in a Discrete-time Risk Model with Dividend Strategy
Junqing Huang *
School of Mathematics, Liaoning Normal University, Dalian, China.
Zhenhua Bao
School of Mathematics, Liaoning Normal University, Dalian, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a discrete-time risk model with dividend strategy and a general premium rate is considered. Under such a strategy, once the insurer’s surplus hits a constant dividend barrier , dividends are paid off to shareholders at instantly. Using the roots of a generalization of Lundberg’s fundamental equation and the general theory on difference equations, two difference equations for the Gerber-Shiu discounted penalty function are derived and solved. The analytic results obtained are utilized to derive the probability of ultimate ruin when the claim sizes is a mixture of two geometric distributions. Numerical examples are also given to illustrate the applicability of the results obtained.
Keywords: Compound binomial model, two-step premium, defective renewal equation, Gerber-Shiu discounted penalty function, dividend strategy.