Improvement Of Risk Models In Different Factors With Interference

Risk theory as an important branch of application mathematics, is a hot topic in the presentactuarial science research． Risk theory provides basic Knowledge for the operator or thedecision—maker to assess risk and predict risk, through the study of the risk models in insurancematters to analyze quantitatively the stability or security for insurance company．Ruin theory as thecore content of risk theory, is an important research direction. Ruin probability research of risk modelsis very active; the research provides a very useful means of early risk warning for decision-makers ofinsurance company. So the study of risk models has important theoretical and practical significance.The classical compound Poisson risk model is a kind of most basic model，but it is just for asingle-type based, and has certain limitation in certain actual problem’s application，the classical riskmodel can’t satisfy financial company needs, so some scholars extend the classical risk mode in manyways, and make the corrected models get more near practical situation.In this paper, we carry on the promotion from several aspects based on the classicalrisk model. First we discuss a new risk model under the condition of the funds rate and theinflation rate. At the same time, the surrender events and the disturbance terms are alsoconsidered. By investigating the nature of surplus process in the risk model, we get theruin probability and the Lundberg inequality of this risk model. Then, we discuss a newrisk model with multi-insurance under the condition of the funds rate and the inflation rate.At the same time, the surrender events and the disturbance terms are also considered. Byinvestigating the nature of surplus process and the nature of the adjustment coefficient R,we get the upper bound of the ruin probability. Finally, according to distracter andby-claim together, we establish a new risk model，where the differential and integralequation for ruin probability and upper bound for the ultimate ruin probability areanalyzed.