Modeling loss reserving in non-life insurance

Abstract

A non-life insurance company has to set aside the right amount of money in order to meet all future liabilities. Failing to do so, the company can become insolvent. One of the oldest actuarial techniques is the Chain-Ladder algorithm. It has been used widely to estimate loss reserving. However it excites controversy since it is not based on any theory until more recently researchers tried to justify it by some theoretical basis. This dissertation studies the approach of generalized linear models applied to loss reserving. In particular, it focuses on the Over-Dispersed Poisson model which reproduce the same reserve estimates as the Chain-Ladder technique. However such models are based on a few data and often assume independence between aggregated incremental claims which therefore do not capture the real dynamics of claim arrivals and payment processes. Then the model is formulated as a marked Poisson point process, the stochastic approach studies individual claims rather than aggregated. These processes are far more realistic since they are based on much weaker assumptions and explain better the dynamics of a non-life insurance portfolio.