In this note we derive the expected total discounted profit of an insurer due to a single policy holder within a third-party liability insurance. We consider both a policy holder claiming optimally and non-optimally.

In this paper we analyse the optimal claim behaviour of a policy holder having a third-party liability insurance in which one is allowed to decide at the end of an insurance year which damages occurred during that year should be claimed. This analysis can only be carried out in detail in case...