Abstract
One of the fundamental activities of insurance companies is the calculation of technical reserves. The available data are usually considered in the form of run-off triangles.
Prediction of unknown values, which are the basis for the calculation of reserves, can be constructed not only using simple approaches such as chain-ladder, but also using advanced methods such as state-space modeling. This paper focuses on the construction of Kalman projections of the values in dependent run-off triangles, which can be considered in the form of a time series with missing observations.
Since the quantiles, currently the preferred risk measure, or even the whole distribution of the reserves are highly important, their estimation using smoothed bootstrap is also the content of this work. The proposed methods are applied to real data consisting of two dependent run-off triangles in order to verify their applicability in practice.
The obtained results are compared to the ones obtained by other procedures.