Ruin probability and joint distributions of some actuarial random vectors in the compound pascal model

Abstract

The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U(T − 1), |U (T )| and inf 0≤n<τ 1 U (n) (i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery) and the distributions of some actuarial random vectors.