http://repository.president.ac.id/xmlui/handle/123456789/11029 2026-04-07T20:01:09Z 2026-04-07T20:01:09Z Rachman, Muhammad Chairul http://repository.president.ac.id/xmlui/handle/123456789/11409 2023-05-05T07:25:35Z 2022-01-01T00:00:00Z

APPLICATION OF THE BAYESIAN ESTIMATION IN PREMIUM RATE CALCULATION OF AUTOMOBILE INSURANCE Rachman, Muhammad Chairul The bonus-malus system is an insurance system that divides premium classes. If a policyholder files a claim in the previous year, a malus or penalty is charged, which increases the amount of premium that must be paid the following year. If, on the other hand, the policyholder does not file a claim in the preceding year, a bonus or discount will be applied to the premium to be paid the following year. The primary goal of this thesis is to develop the bonus-malus premium system as one of the most important tools for improving traffic safety. The Poisson-Gamma and Poisson – Inverse Gaussian distributions will be used to determine the expected frequencies of the observed data in this thesis. The maximum likelihood approach will be used to estimate the parameters, whereas Bayesian estimation method will be utilized to calculate the premium. Throughout this thesis, it has been shown that the Poisson-Gamma and Poisson Inverse Gaussian distributions are appropriate choices in the process of modeling the bonus-malus premium system using a sample from generation data in R packages. The study's key result is the development of a bonus-malus premium table based on the Bayesian estimator, where the net premium is determined using the expected value principle. According to the findings, the proposed premium system could be enhanced by integrating additional priori policyholder characteristics.

2022-01-01T00:00:00Z Febrianti, Ranny http://repository.president.ac.id/xmlui/handle/123456789/11354 2023-05-03T09:32:53Z 2022-01-01T00:00:00Z

CALCULATION OF THE ULTIMATE RUIN PROBABILITY USING LAPLACE TRANSFORM Febrianti, Ranny Estimation of ruin probability is very important in insurance companies. Estimation used to anticipate the possibility of losses that may arise due to risks the unexpected events. In this thesis, the calculation of ruin probability using the Laplace transforms through the calculation of survival probability is discussed with Exponential and Gamma distribution. The numerical results from the three example cases of probability distribution functions show that the ruin probability depend on initial surplus. When initial surplus increase then the ruin probability decrease. This surplus is derived from the reserves of the initial surplus plus a premium amount received by the company multiplied by the number of insurance customers, then reduced by the number of claims issued. The insurance company will be declared ruin if the capital company value symbolized by 𝑈(𝑡) is negative. This research is expected can be a reference and help insurance field.

2022-01-01T00:00:00Z Maulina, Hafshah http://repository.president.ac.id/xmlui/handle/123456789/11353 2023-05-03T09:29:38Z 2022-01-01T00:00:00Z

LOWER AND UPPER BOUND METHOD FOR APPROXIMATING THE PROBABILITY OF RUIN Maulina, Hafshah The probability of ruin is an event that can occur in a company. For instance, the process that can increase risk is trading or investing. While the factors that play a role and influence this event are surplus, premium income, aggregate claims and loss, claim size, interest, security loading, etc. This study can choose several ways to determine the probability of ruin and survival probability. At the same time, this research used a literature study with the numerical method using approaches from three cases that follow the exponential distribution and its variation. Generally, two options can determine the probability of ruin through discrete and continuous time, but this study focuses on continuous time. At the same time, the data used in this study are not original but are made from scratch. This computation of the probability of ruin starts from the surplus process. The approaches that can be used to find out and calculate the process are the Laplace transform, Cramér-Lundberg model, and the distribution of aggregate loss. This study uses the aggregate loss distribution that follows the Poisson distribution and a Compound Poisson distribution to calculate the surplus process. The calculation may draw two models to estimate the distribution of aggregate losses. The models are individual claims or the collective risk model, and this study uses the approach of the collective risk model. The final result of this study will present a table that can compare the results of the lower and upper bound within the exact solution, known as an analytical which able to show how variables and interactions between variables can affect the results of the cases.

2022-01-01T00:00:00Z