Estimasi Aggregate Loss Menggunakan Pendekatan Bayesian Metode MCMC Algoritma Gibbs-Sampling dengan Software OpenBUGS

Melati Sinta Nurdanita; Azizah Azizah

doi:10.37905/euler.v13i3.33769

Estimasi Aggregate Loss Menggunakan Pendekatan Bayesian Metode MCMC Algoritma Gibbs-Sampling dengan Software OpenBUGS

Melati Sinta Nurdanita, Azizah Azizah

Abstract

This study aims to estimate aggregate loss (total loss) in private passenger car insurance data using the Bayesian approach of the Markov Chain Monte Carlo (MCMC) algorithm Gibbs-Sampling with the help of OpenBUGS software. The approach was carried out by modeling claim frequency data using Geometric and Negative Binomial distributions, and claim severity using Gamma and Lognormal distributions. Next, the prior for each model was determined, along with calculations for the likelihood function, joint distribution, marginal distribution, and posterior distribution. Since the resulting posterior distribution could not be calculated analytically, simulation was performed using OpenBUGS software to calculate it. Simulation was also used in predictive posterior calculations to estimate future aggregate losses. The results show that the Bayesian approach with the Markov Chain Monte Carlo method using the Gibbs-Sampling algorithm and its implementation through OpenBUGS software can be used to estimate aggregate loss. From the simulations used, it was found that the estimation of aggregate loss for private passenger car insurance is influenced by the selection of the frequency and severity of claims models. The Negative-Gamma Binomial model produced the highest posterior predictive estimate of aggregate loss at $75270.0, while the Geometric-Lognormal model provided the lowest estimate at $70500.0. Meanwhile, the model with the smallest standard deviation is the Negative Binomial-Lognormal model, which is $62720.0. This study contributes to insurance risk modeling, particularly in determining reserve funds and setting insurance premiums tailored to the target market of insurance companies.

Keywords

Aggregate Loss; Bayesian; Markov Chain Monte Carlo; Gibbs-Sampling; OpenBUGS

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DOI: https://doi.org/10.37905/euler.v13i3.33769