Joint distributions of some actuarial random vectors in the compound binomial model

The compound binomial model is first proposed by Gerber [Gerber, H.U., 1988. Mathematical fun with compound binomial process. Astin Bull. 18, 161-168]. In this paper, we introduce a renewal mass function of a defective renewal sequence constituted by the up-crossing zero points of the model and get its explicit expression. By the mass function together with the strong Markov property of the surplus process {X(n)}, we obtain the explicit expressions of the ruin probability, the joint distribution of T,X(T−1) and |X(T)| (i.e., the time of ruin, the surplus immediately before ruin and the deficit at ruin) and distributions of some actuarial random vectors containing more than three variables.