On the Distribution of the Deficit at Ruin and the Surplus Prior to Ruin in the Compound Binomial Model

We consider the compound binomial model where the safety loading can be positive negative or zero. We give explicit expressions for the joint and marginal distributions of the deficit at ruin and the surplus prior to ruin in the case of negative and zero safety loading .Via change of measure we derive expression for positive safety loading. The expression involve the Lundberg’s coefficient. We show a special relation between the Lundberg’s coefficient and the distribution of the deficit at ruin. We derive also the asymptotic distributions as the initial surplus is big. Examples are given for geometrical claim size distribution and fix claim size.

Keywords: ruin probability, asymptotic distribution, change of measure, geometric distribution, Lundberg coefficient.