NUMERICAL SOLUTION OF RUIN PROBABILITY IN THE CLASSICAL RISK PROCESS USING HEUN’S METHOD

Abstract

Ruin probability is the likelihood that the insurer's surplus will go below zero at some time in the future, or the total claim exceed the sum of initial surplus and the total premium at some time t in the future. Several methods can be used in order to calculate the probability of ruin. In the classical risk model, the ruin probability can be calculated via the integro-differential equation. With analytical method, Laplace transform can be used but the calculation is done manually in order to solve the survival probability. Using numerical method like Euler’s method, it produces a good approximation with some limitations. In this research,

the ruin probability is calculated through survival probability using integro- differential equation with two different approaches. In case where the value of

claim is followed by the Gamma and Exponential distribution, Laplace transform and Heun’s method is used to compare the performance of both methods. From the result of the simulation, it shows that the ruin probability will decrease as the initial surplus increases, while the survival probability will increase alongside. It can be said that the Heun’s method is resulting to a good approximation with the maximum error value at the order of 10−4 when u is [0,60] for the first case and when u is [0,30] for the second case, also at the order of 10−6 when u is [0,100] for the third case. With note that when the value of initial surplus u is bigger, the error value can be greater.