Research About The Numerical Solutions Of The Upper Bound Of The Bankruptcy Probability In Two Types Of Risk Model

In this paper, numerical simulation of the actuarial indicators, e.g. bankruptcyprobability and survive probability of the stochastic processes and random variablesunder specific distribution, in the numerical solution of the upper bound of thebankruptcy probability of two types of financial insurance model is studied. Also, thebankruptcy probability of the risk model, when the two types of claims are dependent orindependent, is numerically analyzed. Meanwhile, the influence of the interferencefactor, interest rate factors, dependency coefficient on the upper bound of thebankruptcy probability is discussed. The structure and content of the paper are asfollows:Firstly, the development history of the risk theory, the achievement of the researchabout the risk theory, and the main purpose and significance of the research are generallyintroduced. What’s introduced in detail is the relative knowledge of the bankruptcytheory about the risk model.Secondly, a simple introduction of some basic concepts, stochastic processes, themethod of the research, and several demonstrations of the Proposition used in the paper isprovided.Thirdly, with the use of MATLAB software, the distribution of some commonactuarial indicators of two types of models, e.g. bankruptcy probability of the dependentrisk model and the influence of the dependency coefficient on the bankruptcy probability,is numerically simulated. First, double insurance risk model, of which the claims processhas both dependencies and with-interest rates, is introduced. Then several previousconclusions of this model in some special circumstances, when the total number of theinsurance policy and the total number of the claims obey the Poisson process of differentparameters respectively are listed. Also the impact of the interest rate factors on bankruptcy probability is studied, after which the numerical simulation is conducted withsome practical examples.Finally, a general summary of this paper is made, and the work we are going tocarry out on the basis of this paper has been pointed out.