The Compound Pascal Model And Some Conclusions In Stochastic Environment

In the present actuarial science and mathematical research, risk theory is a hot topic, and ruin theory is the core of risk theory. The study of the ruin theory started from the PhD thesis of Lundberg, who was a Swedish actuarial scientist in 1903. In the paper, he first introduced an important stochastic process, Poisson process. At first people use stochastic processes to study compound Poisson risk models, discuss the ruin probability and the joint distribution of deficit at ruin, surplus immediately before ruin, the time of ruin and other actuarial diagnostics. As the financial market develops and the environment of business changes, the classical risk model has a lot of restrictions with the reality of the insurance companies.In this paper, we first use the strong Markov property to study the ruin probability and the joint distributions in the compound Pascal model; then we consider the ruin time, the ruin probability and the joint distributions in the Pascal model with constant interest; finally we consider the Pascal model with a Markov-modulated interest and a Markov-modulated premium rate, then we study the ruin probability, the joint distributions and the upper bounds of ruin probability in the model with a constant premium rate and a Markov-modulated interest.