LOWER AND UPPER BOUND METHOD FOR APPROXIMATING THE PROBABILITY OF RUIN

Abstract

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.