Premium Estimation Using a Spliced Gamma-Gamma Distribution for Long-Tail Insurance Claims

Abstract

Determining fair premiums that accurately reflect actual risks is a crucial element in insurance risk management, particularly when claim data exhibits long-tail characteristics that are challenging to model using a single distribution. This study aims to develop a premium estimation model using the spliced Gamma-Gamma distribution, which can capture the behavior of small to large claims more flexibly. This model is applied to a collective risk model framework, focusing on calculating the expected value and variance of aggregate claims as the basis for premium estimation. Premium estimation is conducted using three actuarial principles: the expected value principle, the variance principle, and the standard deviation principle. The research indicates that the standard deviation principle yields the most accurate premium estimation, as it accurately reflects the risk level while striking a balance between premium adequacy and affordability for policyholders. This approach considers both the expected loss and its volatility, making it more adaptive to extreme claim risks. This study demonstrates that claim modelling using splicing distributions, combined with volatility-based premium estimation principles, can be a practical and realistic approach to managing risk and estimating premiums more accurately.