A Study On Some Problems In Risk Pricing Of Actuarial Theory

Human social life are often faced with illness, death, accidents and natural disasters risks. Scientific and technological development and improvement of living standards, and constantly enhance the human ability to resist risks, but the risk is simply impossible to avoid. With the social, economic and scientific and technological development, but also can has created new risks, for example, a modern traffic accidents, environmental pollution, nuclear leaks, AIDS, the market fluctuations and so on.The risk in local or on microscopic has the uncertainty and the loss centralized characteristic, but in wide range and on macroscopic, it also has the stability and the uniformity, namely the risk occurs possibility roughly stable as well as loss size basic obedience certain distributed rule. The basic principle of insurance is to focus on a number of premium of the insured at the insurer, when the risk occurs, by the insurer to bear the loss. This mechanism allows the insured to pay a small amount and a fixed premium, the loss of a large number of uncertain transferred to the insurer or insurance companies. Insurer use premium income on the one hand to ensure the normal operation of the compensation, on the other hand, through the analysis and calculations to a reasonable allocation of funds, improve the insurance fund investment returns and ultimately harvested both the insured and the insurer.Actuarial science is based on modern mathematics and mathematical statistics, which is the tools of insurance industry to quantitative analysis for management of insurance in all aspects.Actuarial science can improve management, develop strategies and provide scientific basis for management decision-making in insurance industry. it has become an important factor for insurances to survive and develop in the fierce market competition.Credibility model is an empirical model of assessing fees. In this process, the actuary based on previous individual or a group of risk experiences to adjust future insurance premiums. In actuarial science, a lot of problems need mathematical model to predict future insurance costs, particularly in the short term. Therefore, credibility theory known as the cornerstone of modern actuarial science. The study of credibility theory has been very mature in the abroad. In particular, in recent years, modern statistical theory and traditional credibility model combining to produce a lot of credibility models,which are both depth theoretical and practical value,has opened up a broader space for the application of credibility model in the actuarial science. Equity-linked life insurance is one of modern life insurance, which occurred more than 30 years, but only more than 10 years in China, which is not as widely recognized and accepted by people. A few Chinese scholars is study it and mostly qualitative research. The emergence of Equity-linked life insurance in China has gone from hot to a halt and then to return the tortuous development process.Whether they appear in line with China's insurance market needs, how to develop the insurance and how it is rational pricing becomes the focus of attention, with a very important theoretical and practical significance.Risk model is a stochastic model of loss or settlement of claims on the X. Risk models are insurance products, but also non-life insurance product design and theoretical basis for the insurance business. According to whether to consider the time factor, risk models can be divided into long-term risk model and the short-term risk model.According to the total number n of the policy is random or not, risk models can be divided into aggregate risk model and the individual risk model.According to the total number n of the policy being considered in the cycle is random or fixed, risk models can be divided into closed or open risk models.This paper studies the pricing of insurance risks. In the credibility model, the parameters and random effect of Buhlmann - Straub credibility model are researched.Two-stage estimate was used to estimate the parameter and F-test is used to test the random effect.In two-stage estimate,used orthogonal transformation to estimate aggregate average and fitting constants method to estimate variance which is unbiased.Under regression sum of squares to get the F-test statistic in order to test the random effect, the power of the test is increasing function of the test variance.The parameters of regression credibility model with linear trend are estimated and test. Orthogonal transformation is used to estimate parameter and unbiased estimate of parameters are obtained.Likelihood ration test is used to test randomness and linear trend.The better P-value of likelihood ration test is got and Monte-Carlo simulation is performed.In the Equity-linked life insurance, in the initial reserve yield fixed or random circumstances, by considering the distribution of Reserves and risk compensation for insurance ,the pricing and initial reserve of Equity-linked with the nature of the death payment and pension-linked are discussed,which broadening the Equity-linked life insurance research results and research methodologies.In the risk model, double binomial risk model with random interest is discussed.We derive the expressions of the distribution of the surplus immediately before ruin,the distribution of the time in the red which describe the severity of ruin,the recursive formula for finite time ruin probability and the integration equation for ultimate ruin probability. Upper bound for the ultimate ruin probability, the recursive formula for the joint distribution of surplus immediately before ruin and deficit at ruin are derived.