| As the economy continues to develop,the role played by the insurance economy becomes more and more obvious and has attracted extensive research.Risk analysis is of great importance to insurance companies because,on the one hand,they generate income through premiums,but on the other hand,the uncertainty of future insurance claims makes them subject to certain risks in their operations and even the possibility of insolvency.The probability of insolvency is a key indicator for assessing an insurer’s risk profile and risk managers can use historical data to extract different models of insurance risk,including premium income,claims,investments and other indicators.Using this as a basis,the risk manager uses the proposed models to calculate and forecast the insurance company’s probability of insolvency,and finally uses the probability of insolvency to analyze the insurance company’s risk and make recommendations accordingly.The probability of insolvency can be divided into finite-time probability of insolvency and infinite-time probability of insolvency.The infinite-time probability of insolvency is not available at a specific point in time and has certain limitations,therefore the study of the probability of insolvency in this thesis is based on the finite-time probability of insolvency.In this thesis,the classical Cramér-Lundberg risk model and the premium stochastic risk model are used to simulate the risk process of insurance companies.Firstly,the large deviation theory（LDP）is applied to obtain an approximate estimate of the probability of insolvency of an insurance company,and the specific values of the probability of insolvency can be obtained by assigning parameters.It is worth noting that in the process of applying the large deviation theory to calculate the probability of insolvency,the rate function of claims is required,but the rate functions of many distributions are difficult to obtain.To address this problem,this thesis develops a minimum fork entropy model to find the rate function in large deviations,which is then substituted into the large deviation results to further obtain the probability of insolvency of an insurance company.Secondly,we also use the precise large deviation theory to obtain the insolvency probabilities of insurance companies under two risk models and assign values to the parameters to obtain the specific insolvency probabilities of insurance companies with claims following Weibull distribution.The thesis concludes with an evaluation of the probability of insolvency results using the mean squared error metric for both large and precise large deviations.Firstly,when the claims are exponentially distributed,the known findings of the insurance actuarial science are compared with the results of the large deviation case and the mean squared error is calculated to be4.416×10-10,which is a small difference.Secondly,the thesis calculates the results of the precise large deviations of the exponential distribution of claims,and compares the insolvency probability results with the actuarial results and computer simulations,and obtains mean squared errors of 0.064 and 0.098 respectively,both of which are significantly different.The mean square error between the bankruptcy probability results obtained using the fine large deviation method and the computer simulation results is6.463×10-5,which is less,indicating that the fine large deviation theory is more applicable to the calculation of bankruptcy probability when the claim amount follows the Weibull distribution. |
