Studies On Multi-insurance Random Risk Models

With the development of the times, risk factor is more and more complex, the study of risk theory has become more important. Ruin theory is the core content of risk theory, this article is devoted to study ruin probability problems of multi-insurance models on the basis of the classic risk model and its extended models. Providing the actural theory basis for insurance company to reduce the ruin probability.Aiming at this kind of model, we analyze the ruin problem mainly from the following two aspects:First, considering insurance company will put extra capital into the financial markets, in order to improve the ability of payment and avoid ruin, at the same time, considering the interference factors have influence on insurance companies, a kind of multi-insurance risk model with investment and interference was founded, the premiums and claims follow the compound discrete Poisson distribution. Using conditional expectation and stochastic process theory to discuss the nature of model, obtaining the general expression of ruin probability and Lundberg inequality. And when the premium and cliam both obey the exponential distribution, the change trends of the upper bound of ruin probability along with premium, investment and claim were founded; Then, the compound poisson model was extended to the compound binomial distribution model, researching the compound binomial risk model with investment and interference, using the method of martingale analysis obtained the general formula for the ruin probability and Lundberg inequality.Secondly, considering stochastic interest rate and inflation rate have influence on the economic benefits of insurance company, a kind of multi-insurance risk model with interference under the stochastic interest rate was established, we research this kind of model’s ruin probability with two kinds of distributions: first, assuming that the premiums and claims follow compound binomial distribution and the premium was composed of fixed premium charging at a constant rate and random premium, a multi-insurance risk model with compound premium under random interest rate was founded. secondly, the compound binomial model was extended to compound negative binomial model, at the same time, considering the investment process and interference factors, a kind of multiple risk model with investment and interference under stochastic interest rate was studied, using the stochastic theory to study the two types of models such as martingale, their ruin probability and upper bound were obtained respectively, in the end we give the change of ruin probability along with interest rate and inflation rate.