The Study Of Ruin Probability In Some Risk Models

The calculation of ruin probability is regarded as the classical problem of the Actuary Science. Problems of ruin probability of the original insurance company are dealt with for some risk process models in this paper, the concrete contents are as follows:First of all, based of the risk model with two compound Poisson processes, we consider an interference item; the Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory. The integral representations of the nonruin probability and the integral-differential equation of the nonruin probability in finite time are gotten.The next, we consider a risk process with positive and negative risk sums, we derive the integral equation for the ruin probability. We obtain the exponential inequality for the ruin probability. Two examples are given to show the numerical results.The third, a renewal process risk model is built up. In this model, the interest rate at any time continuous variety, the distribution of the claim size obey to Pareto distribution, the number of the claim times obey to renew process and the claim-arrival obey to Erlang process. The approximate expression of the finite time ruin probability of the insurance company is acquired.The last, the risk model with compound Poisson-Geometric process and interference item and its penalty function are studied. Based on this model we discuss the penalty function, and give the integral-differential equation for it. Finally, the explicit expression of Laplace transform of the penalty function is obtained.