The Study On Ruin Probability And The Optimal Control For Some Risk Models Under Different Aspects

We get some generalized risk model by extending the classic risk model in some different aspects and do some reseaches on them. And a type of new and practical risk model was proposed. The thesis mainly constants the following results.First, by taking into the composite rate in insurance business, with premiums'policy influencing the number of claims, a new and practical multitype-insurance risk model which is described by Poisson process and Poisson-Geometric process is proposed to extend the classical one. After analyzing the proposed model, the formula of ultimate ruin probability is derived. Finally, various trends of the upper bound of ruin probability are simulated analytically along with changing premium size, claim size and parameter P. This clearly reflected the relations between the various and the ruin probability. The results have the important significance.Secondly,under the discrete time, a new and practical risk model which is the ruin probability of the Compound Non-Binominal risk model was introduced by considering the refund event of insurance company and the appropriation budget, then analyze the compound binomial risk model for same conditions, by the martingale method, getting the similar conclusions to the above.Thirdly, a new and practical bivariate risk model is proposed to extend the classical one. And the ruin probability which is different from the classical risk model is defined. Furthermore using some results of one-dimensional risk processes, the ruin probabilities for two-dimensional risk model which is studied on the assumption that is built correlated is obtained.Lastly, the mode of the investment was improved. The investment includes not only the riskless asset, but also the risky asset. By the improvement, the stock market theory was introduced into the risk theory. It is more Practically according with the development of the finance. In this Part, using the optimal control of the stochastic control theory, we set up the HJB function of this kind of risk model. We can obtain the optimal strategy of investment in order to make the ruin Probability being least. Finally, various trend of the optimal strategy is simulated analytically along with changing many parameters, and the results are heuristic to operate the insurance business.