RUIN THEORY OF INSURANCE PRODUCTS USING THE CRAMER-LUNDBERG MODEL WITH THE ADDITION OF INVESTMENTS

• Main Author: Islami, Firman
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/85676
• Institution: Institut Teknologi Bandung

Ruin Theory has been developing since 1903, eventually leading to the creation of the Cramer-Lundberg Model in 1930 to analyze an insurance company's need to meet all its financial obligations. However, from 2009 to 2024, at least six cases of insurance company defaults occurred in Indonesia, with amounts ranging from billions to tens of trillions of rupiah. This report discusses the mathematical structure of the Classic Cramer-Lundberg Model, which is frequently used in the insurance industry. This simple model includes initial capital, a fixed premium rate, and an assumed claim distribution. It is derived that the survival probability of a company increases with higher initial capital. Furthermore, if the premium rate does not meet a criterion known as the “net profit condition,” the probability of bankruptcy will be 100% for a surplus process that continues indefinitely. The report also explores the Cramer-Lundberg Model with three common claim distributions: Exponential, Hyper-exponential, and Erlang. Theoretical curves will be verified through simulations written in R. It is found that the simulation results align with theoretical results, both without investment and with investment. Additionally, it is observed that the addition of investment can increase the probability of survival even with a negative premium loading value.