Contributions to RBNS Modelling

Abstract

Reserving against future claims and settlements is vital for insurance companies, in the sense that it influences how they may price their products and the solvency of the insurance company. This thesis will present and compare two models that can estimate the outstanding liabilities: The well known and well used Chain Ladder model which uses aggregated data and the Kaminsky approach that divides the problem into modelling counts and losses separately and regard the delay in IBNR and RBNS as multinomial phenomenon governed by delay probabilities. Mean square error will be used to compare these methods. The thesis will provide a theoretical basis for each method and an analysis when implemented on fire and car insurance data provided by a Norwegian non-life insurance company. A large portfolio approximation will be done analytically, which will confirm with the observation done in the numerical study that for large portfolios it will be more accurate to model claim counts and sizes separately than using aggregates to estimate the outstanding liabilities. The more heavy-tailed the claim size distribution is, the more superior will the Kaminsky approach be.