Studying Of Ruin Probability About Dual Poisson Model

In studying of insurance risk theory the finite time ruin probability, the eventual ruin probability and the related issue about insurers are main topics to study. In this paper, based on the classic surplus model we discuss the model with premium income process also being a compound Poisson process, viz. the dual Poisson model with continuous timeU(t)=u+C(t)-S(t) t0and the dual Poisson model with discrete timeU(n)=u+C(n)-S(n) n=0,1,2,…where we denote the initial reserve by u=U(0), and refer to S(t) or S(n) as a compound Poisson process with the parameter and distribution F(x) by which we denote the overall claim amount, and C(t) or C(n) also as a compound Poisson process with the parameter and distribution G(x) by which we denote the overall premium , respectively, in (0,t] or (0,n]. There are the meanings of theory in the paper. Firstly, the ruin probability is very important for the insurer to measure the risk. Secondly, in practice, the insurers need the model that is closest to the realities so that the risk can be measured well and truly. The dual Poisson models are better than the classic surplus models with regard to this need. Through the studying of the dual Poisson model, we find the integral equation of the eventual ruin probability that is +about the continuous time model in the first chapter of the paper. As the premium of individual guarantee slip is a constant and the individual claim amount is discrete random variables with non-negative integer values, we find the recursive calculation formulas of the eventual ruin probability that arewhere =P(X=x). And we also find the calculation formula of the eventual ruin probability that is= + + for the continuous time model with the individual claim amount X exponential and the premium of individual guarantee slip Y tail-cut exponential distribution. In the second chapter, our work is also about the continuous time model. As the premium incomes and the individual claim amounts are discrete random variables with non-negative integer values, we find the calculation formulas of the finite time ruin probability that are == k2=1-P(u)and the calculation formula of the eventual ruin probability that is=by means of using transition probability. In the third chapter, we discuss the discrete time compound Poisson model with premium income process also being a compound Poisson process. As the premium incomes and the individual claim amounts are discrete random variables with non-negative integer values, we find the calculation formulas of the finite time ruin probability that are = k=1,2,3,….=d[and the calculation formulas of the eventual ruin probability by using transition probability= k=1,2,3,….=d[.