Some Popularizations On Risk Models

Risk theory is one of the main component of actuarial science, and is also one of thecurrent hot topic of mathematical research. Researches on ruin probability are the mainissue of ruin theory. In order to research the ruin probability and its related problems better,researchers established the classical risk model. However, the classical risk model is arelatively ideal mathematical model, which itself has many defects. So, on the basis of theclassical risk model, this paper improves and popularizes and establishes a new risk modelwhich is better fit for the modern insurance company operating system.First of all, in the classical risk model, the times that premium is received areconsidered as a homogeneous Poisson process, and the mean character of a homogeneousPoisson distribution is mean equal to its variance, but in practical, there is a situationexisting that mean is greater than its variance. In view of this situation, this paper willimproves the compound Poisson process to compound PG process. Establish thecompound PG risk model, and consider the premium collection times as a Poisson process,and the premium received every time considered a random variable following exponentialdistribution. Explain the practical significance of making this popularization, and aftercalculation, get the adjustment coefficient and the bankruptcy probability of the risk modelmentioned.Secondly, in the practical insurance, risk events and settlement of claims are notnecessarily equal. In this respect, this paper discussed the risk model under the conditionthat claims are deductible. In the research, we assume that the times of claims are Poissonprocess and the loss distribution is an exponential distribution. With the help of classicalrisk model related conclusion, get the relatively safe load, adjustment coefficient and thebankruptcy probability under the condition of deductible claims.In addition, this paper has a study of discrete time risk model. Use a negativebinomial random sequence to replace a traditional homogeneous Poisson sequence.Establish the compound negative binomial risk model, and discuss the significance of the model. What’s more, deduce the formula of the ultimate ruin probability, and at last, withthe help of the contact between the compound Poisson process and the compound negativebinomial process, get the ruin probability of compound negative binomial risk model. Inaddition, based on the compound negative binomial risk model, considering randomdisturbance factor and extra capital for investment to improve the insurance companysolvency, make the original compound negative binomial risk model more close to thepractical situation, and better guide practical insurance.