Deficit At Ruin On A Class Of Markov-Modulated Risk Model With Multiple Insurance

Risk theory is mainly that how to make use of the methods of probability and stochastic process to establish mathematical model,on the basis of some practical problem,which face the insurance company.In the article,a class of Markov-Modulated Risk model with Multiple Insurance is introduced,which is based on the classic risk model.Within infinite time,firstly,a integral equation for the distribution of deficit at ruin is obtained under the initial state is given.Then,one-dimensional Laplace transform is taken on the two sides of the equation.Furthermore,after solving the system of equation transformed,its Laplace transform is given.When the claim is exponentially distributed and there are two states,inversion of the Laplace transform is used to get the expressed equation of the distribution function of deficit at ruin and ruin probability of the model.Within finite time,a integro-differential equation is got under the initial states is given.Then,two-dimensional Laplace transform is taken on the two sides of equation.Because of the difficulty of solving the inversion of the Laplace transform of the distribution function of deficit an ruin,stochastic simulation is introduced to analyze the model.After analyzing the algorithm of simulation and approximating the number of simulation,some data of simulated mean of deficit at ruin is got on the different condition,on the basis of which the distribution figure of deficit an ruin are obtained on the different condition with finite time.Finally,after observing and analyzing the data and figures,some statistical rules are obtained.