Abstract: The fully discrete binomial risk model are considered and the probabilities of the following events are discussed in this paper: the insurance company survives up to any fixed time n, the insurance company survives up to any fxed time n and the surplus at time n equals x( x≥0) . Finally, the probabilistic laws of the following events are gotten: (i) the index of the claim which causes the ruin, ( ii) the deficit at ruin.

Key words: compound binomial model, survival probability, deficit at ruin