Solving the ruin probabilities of some risk models with Legendre neural network algorithm

Abstract

This paper studies a numerical method based on Legendre polynomials and extreme learning machine algorithm to solve the ruin probabilities in the classical risk model and the Erlang(2) risk model. In our method, the hidden layer is eliminated by expanding the input pattern using Legendre polynomials. The network parameters are obtained by solving a system of linear equations using extreme learning machine algorithm. The numerical experiments of some risk models under exponential distribution and Pareto distribution have been performed to validate the accuracy and reliability of our proposed Legendre neural network algorithm. Compared with the existing method, the results obtained by our proposed Legendre neural network model can achieve very high accuracy. Legendre neural network algorithm is well suited for solving the ruin probabilities of the risk models.