A multi-state approach and flexible payment distributions for micro-level reserving in general insurance

Insurance companies hold reserves to be able to fulll future liabilities with respect to the policies they write. Micro-level reserving methods focus on the development of individual claims over time, providing an alternative to the classical techniques that aggregate the development of claims into run-o triangles. This paper presents a discrete-time multi-state framework that reconstructs the claim development process as a series of transitions between a given set of states. The states in our setting represent the events that may happen over the lifetime of a claim, i.e. reporting, intermediate payments and closure. For each intermediate payment we model the payment distribution separately. To this end, we use a body-tail approach where the body of the distribution is modeled separately from the tail. Generalized Additive Models for Location, Scale and Shape introduced by Stasinopoulos and Rigby (2007) allow for exible modeling of the body distribution while incorporating covariate information. We use the toolbox from Extreme Value Theory to determine the threshold separating the body from the tail and to model the tail of the payment distributions. We do not correct payments for in ation beforehand, but include relevant covariate information in the model. Using these building blocks, we outline a simulation procedure to evaluate the RBNS reserve. The method is applied to a real life data set, and we benchmark our results by means of a back test.