The Application Of Monte Carlo Method In Actuarial

Actuarial science is an interdisciplinary science based on probability theory and mathematical statistics, which is combined with financial and economic principles for prediction, analysis, assessment and management on risk in insurance, finance, investment and financial fields. In the 40's of last century, physicists created the Monte Carlo method. Then after the development for half a century, the Monte Carlo method had been applied to various areas of scientific computing. From the 1980s, statisticians had used the Monte Carlo Method into the nonparametric statistical inference, maximum likelihood estimation, Bayesian model and other fields. And Markov chain Monte Carlo ( referred to as MCMC ) method is the most widely used one.In this article, I choose the mortality rate smoothing in life insurance, which is related to the mortality in premiums calculating. Then improve the four rank maximum entropy optimization model into five rank. And use the conjugate gradient method and Monte Carlo method to solve the model and comput it. The results obtained in the article are compared with maximum likelihood and Bayesian methods, we can see that the results which is smoothed by Monte Carlo method combined with the conjugate gradient method, is better than the other two methods and is more fitting the sample data. Thus proves the effectiveness of solving such problems by Monte Carlo method.This article also researches some problem in the automobile insurance in the non-life insurance, and calculates the posterior distribution of the claims frequency and posterior estimates of the missing parameter values by MCMC simulation. In the case of incomplete historical data, uses WinBUGS package to find the posterior distribution of the claim frequency parameters and the estimate of the correlation parameters. The results obtained show that the model not only to make up for the traditional model, but also improving the accuracy of the calculation. And have a practical significance for improving the determining experience rating in automobile insurance.