Joint Distributions Of Some Actuarial Random Vectors In The Continuous-Time Compound Binomial Model

The main aim of this paper is to study the joint distributions of some actuarial random vectors in the continuous-time compound binomial model.The continuous-time compound binomial model, firstly proposed by Liu GX, Wang Y, Zhang B~[13], is the continuous-time version of the compound binomial model with discrete-time, and its limiting case is the classical risk model. In order to get the joint distributions we introduce a defective renewal sequence constituted by the up-crossing zero points and derive its mass function. By the mass function together with the strong Markov property, the explicit expressions of the ruin probability and the joint distributions of some actuarial random vectors composed of the ruin time, surplus immediately before ruin, severity of ruin, maximum surplus before ruin, maximum deficit from ruin to recovery, maximum surplus and deficit before leaving deficit ultimately in the continuous-time compound Binomial model are obtained.This paper includes four chapters. The first chapter is introduction. In the second chapter, the continuous-time compound binomial model and some useful results are introduced. In the third chapter, a sequence of up-crossing zero points and the renewal mass function of the sequence are defined firstly. Then the joint distributions are derived. Further, the corresponding joint distributions are directly obtained for the compound binomial model which is the 1-skeleton chain of the continuous-time compound binomial model. Finally, a special case is considered. The last chapter gives a conclusion.