Numerical Solution Of Ruin Probabilities In Insurance Risk Model Based On Neural Network Algorithm

Risk theory takes probability statistics as the main research tool,by establishing and studying risk model,quantitatively characterizes the risk faced by insurance companies,and provides support for risk measurement and control in insurance operation.The ruin probability is an important index to measure the risks faced by insurance companies.Insurance companies usually establish a corresponding insurance risk model through premium income,claims,reinsurance,investment and dividends,etc.,the ruin probability is estimated or calculated so that the ruin probability can be used to measure or control risk.However,in many risk models,Mostly the integro-differential equation equation of the ruin probability can be obtained,and it is difficult to obtain the explicit solution of the ruin probability.especially when the claim amount follows the heavy-tailed distribution,can only obtain the asymptotic estimation of ruin probability,which often does not meet the requirement of precision in practical application.However,some traditional numerical algorithms of ruin probability,such as Monte Carlo simulation,can not take both speed and accuracy into account.In this thesis,a new method based on neural network is proposed to calculate the ruin probability of insurance risk model,the integro-differential equation equation of the ruin probability is used to obtain the numerical solution of the ruin probability with high accuracy,and the accuracy and applicability of the method are further improved based on the differential equation theory.This thesis starts from the Erlang(N)risk model.First,based on the integro-differential equation equation of the ruin probability,this thesis use the general ELM(Extreme Learning Machine)algorithm to numerically solve it.In this algorithm,some parameters of the neural network are randomly generated,the activation function is unknown,and it is a general and stochastic algorithm of ruin probability,which can solve the ruin probability under any claim distribution,compared with Monte Carlo simulation,it can obtain the ruin probability with high accuracy more quickly.Secondly,for the problems caused by the initial conditions of the ruin probability,this thesis proposes to use the TFC(Theory of Functional Connections)method to transform the ruin probability into the form of constraint expression,and then to approach the free function through the ELM neural network,then the numerical free function is used to calculate the ruin probability through the constraint expression.This can not only further improve the accuracy,but also improve the applicability of the method.By comparing the numerical errors of different methods,the accuracy of the optimal solution is much higher than that of other existing methods.Finally,an example of numerical calculation of ruin probability under heavy-tailed claims distribution is given to illustrate the applicability of this method.