ACTUARIAL MODELING WITH MARKOV CHAIN MONTE CARLO AND OPENBUGS

• Main Author: (NIM : 20814019), AZIZAH
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/21365
• Institution: Institut Teknologi Bandung

The determination of the correct prediction of claims frequency and claims severity is very important in an insurance business in order to determine the outstanding claims reserve which should be prepared by an insurance company. One approach which may be used to predict a future value is the Bayesian approach. This approach combines the sample and the prior information. The information is used to construct the posterior distribution and to determine the estimate of the parameters. However, in this approach, integrations of functions with high dimensions are often encountered. In this Thesis, a Markov Chain Monte Carlo (MCMC) simulation is used using Gibbs Sampling algorithm to solve the problem. The MCMC simulation uses ergodic chain property in Markov Chain. In Ergodic Markov Chain, a stationer distribution, which is the target distribution, is obtained. The MCMC simulation is applied to three models: Hierarchical Poisson Model, Arbitrary Discrete Distribution, and Grouped Size of Data Loss. The OpenBUGS software is used to carry out the tasks. The MCMC simulation in Hierarchical Poisson Model is able to predict the claims frequency. In Arbitrary Discrete Distribution modeling, the MCMC simulation is able to predict the number of policies which might produce certain claims and is able determine an appropriate model for the data. In modeling the Grouped Size of Data Loss, the MCMC simulation may be used to predict the claims severity in grouped data.