In-sample forecasting: structured models and reserving

Abstract

In most developed countries, the insurance sector accounts for around eight percent of the GDP. In Europe alone the insurers liabilities are estimated at around e900 billion. Every insurance company regularly estimates its liabilities and reports them, in conjunction with statements about capital and assets, to the regulators. The liabilities determine the insurers solvency and also its pricing and investment strategy. The new EU directive, Solvency II, which came into effect in the beginning of 2016, states that those liabilities should be estimated with ‘realistic assumption’ using ‘relevant actuarial and statistical methods’. However, modern statistics has not found its way in the reserving departments of today’s insurance companies. This thesis attempts to contribute to the connection between the world of mathematical statistics and the reserving practice in general insurance. As part of this thesis, it is in particular shown that today’s reserving practice can be understood as a non-parametric estimation approach in a structured model setting. The forecast of future claims is done without the use of exposure information, i.e., without knowledge about the number of underwritten policies. New statistical estimation techniques and properties are derived which are build from this motivating application