Research On Ruin Probability Of Several Kinds Of Risk Models With Interest

In the research field of Insurance Actuarial,the development of Risk Theory is extremely rapid.The related research is basically the transformation and extension of the classic model,so that the model is more close to the reality and the result is more operable.One of the major features of the classic model is that it doesn't involve the process of investment and only describes the process of collecting premiums and settling claims of insurance companies.However,with the development of financial market,financial instruments are becoming more and more varied.Investment has become a necessary work in the daily operation of insurance companies and one of the main sources of corporate profits.Therefore,in this paper,the important impact of the investment factors on the ruin probability will be considered,and the classic risk model will be improved for the further research.Three kinds of risk models are mainly researched in this paper,the first is a compound Poisson distribution risk model with random interest.In the model,the process of premiums is improved to satisfy the Poisson distribution;the second is a compound binomial discrete risk model with Markov chain interest.In the model,the Markov chain interest is introduced to simulate the interest rate changes in the reality in the case of discrete time,and the process of claims of the classical discrete time risk model is improved to satisfy binomial distribution and the amount is random;the third is a double type-insurance compound binomial discrete disk model with Markov chain interest.In the model,the process of premiums and claims and the types of insurance of the classical discrete risk model are improved,with two types of insurance introduced and the binomial distribution satisfied by the process of premiums and claims.Mathematical tools such as probability theory,martingale theory and stopping time theorem are mainly used in this paper to get the expression of the adjustment coefficient and the upper bound of ruin probability for each model.Furthermore,in the research of the two discrete time risk models,the integral expression of the probability of ruin is derived using the methods of mathematical deduction including equivalent transformation and total probability formula,and the conclusion that the upper bound of the probability of ruin is superior than that of classical discrete risk model which do not include investment is proved.Finally,through the comprehensive analysis of the paper,the main research results of this paper are derived and the development direction of the research is given.