Numerical solution for ruin probability of continuous time model based on neural network algorithm

Abstract

In the classical risk model, the ruin probability satisfies the renewal Integro-differential equation, which only has an analytic solution when the claim distribution obeys the exponential distribution. In this paper, due to the characteristics of the existence of initial conditions for the equations, by using the modern artificial intelligence and machine learning theory, we construct a neural network model, in which trigonometric function serves as the activation function. Then, based on the thinking of ELM algorithm, at the same time, different from the classic ELM algorithm, the initial condition of the equation are added to the solver model, and the improved ELM algorithm (IELM) are designed. Finally, through some numerical experiments by using Matlab programming, the numerical solutions of the integral Integro-differential equation under arbitrary claims distribution at any time have been obtained. Through the comparison of numerical solutions with the analytical solutions and traditional numerical solutions, the feasibility and superiority of the proposed IELM algorithm are clearly proved.