Calculation And Algorithm Of Insurance Risk Ruin Probability In Actuarial

The risk guarantee provided by the insurance company plays an important role in the development of the national economy.With the development of modern society,the insurance market has become more and more complex,resulting in many internal and external factors that form a risk intertwined with many uncertainties.This has brought new challenges to the management and control of insurance risks,and its bankruptcy will certainly have a serious impact on society.How to measure the risks faced by insurance companies in a complex market environment is a core issue that must be solved by modern actuarial science.The ruin probability is an important indicator for measuring the risk of insurance companies.Usually,risk managers first propose different insurance risk models based on the characteristics of historical data,such as premium income,claims,investment amount and instantaneous surplus balance of insurance business;and then the ruin probability of the risk model is calculated and forecasted.Finally,to achieve the purpose of controlling the risk,the ruin probability value is used to measure the overall risk of the insurance company.However,for the vast majority of risk models,we can only reach the integro-differential equations for which the ruin probability is satisfied,or the infinite series solutions for the ruin probability.Besides,these integro-differential equations are generally very complex.And there are few precise ruin probabilities,which obtained only when the claim is an exponential distribution or a finite discrete distribution.For the heavy-tailed claims,only a numerical solution could be acquired.Moreover,the traditional numerical methods of differential equations,such as Euler's method,finite element method,etc.,which also have some obvious shortcomings.Under such circumstances,and in terms of timely and effective access to accurate ruin probability,this paper proposes the use of modern artificial intelligence techniques to solve the difficulties encountered in solving numerical solutions for integro-differential equations satisfied by ruin probability,and proposes time series to predict the ruin probability and integro-differential equations for a numerical solution of the ruin probability under optimal structure neural networks.The details are as follows:Firstly,aiming at the characteristics of the ruin probability in the renewal risk model ofErlang(n)satisfies renewal integro-differential equations,Improved l Trigonometry Extreme Learning Machine(ITELM),which with trigonometric function as the activation function,has been proposed for the first time.In the algorithm,the initial value of insurance risk' ruin probability is put into the linear solver,and the advantage of the trigonometric function as an excitation function is proved.In addition,under the same conditions,by comparing with the numerical solution of LS-SVM algorithm,the performance of ITEL algorithm is better,and the numerical solution results obtained are closer to the displayed solution(exact solution)with less error,higher reliability.Besides,it can solve the numerical solution to the ruin probability at any time when the claim is subject to an integro-differential equation under arbitrary distribution conditions.It thus fully explains that insurance risk managers can adopt this technique to obtain the value of bankruptcy probability.Secondly,for the phenomena of overfitting and instability in neural networks,this paper analyzes the causes of overfitting and instability of neural networks,finding that the optimal neural network(NNS)architecture is related to the three objective measures of minimizing root mean squared error(RMSE)for training and testing and minimizing the test error variance(TEV),and a multi-objective Optimized Neural Network Architecture Avoiding Over-fitting(ONNAAO)is proposed,and the existence and uniqueness of the optimal solution of the algorithm is proved.Through empirical comparison with several traditional time series algorithms in several performance indicators,the ONNAAO algorithm is worthy of promotion,and has high credibility,which is suitable for realizing the time series prediction of premium income,compensation,surplus and ruin probability.This could provide technical support for insurance risk managers to effectively prevent and control risks.Finally,combined with ONNAAO algorithm and ETELM algorithm ideas,an Improved Optimal Trigonometry Extreme Learning Machine(IOTELM)with optimal neural structure is innovatively established.Based on the IOTELM algorithm,a series of experiments in Chapters 2 are reworked.By comparing the error data in the table and the image,it has found that the ruin probability obtained by the optimal neural network structure is closer to the display solution(exact solution)and has high credibility.It fully explains that insurance risk managers can adopt this technique to obtain a numerical solution to ruin probability.