Abstract
This paper gives a detailed overview of the current state of research in relation to the use of state space models and the Kalman-filter in the field of stochastic claims reserving. Most of these state space representations are matrix-based, which complicates their applications. Therefore, to facilitate the implementation of state space models in practice, we present a scalar state space model for cumulative payments, which is an extension of the well-known chain ladder (CL) method. The presented model is distribution-free, forms a basis for determining the entire unobservable lower and upper run-off triangles and can easily be applied in practice using the Kalman-filter for prediction, filtering and smoothing of cumulative payments. In addition, the model provides an easy way to find outliers in the data and to determine outlier effects. Finally, an empirical comparison of the scalar state space model, promising prior state space models and some popular stochastic claims reserving methods is performed.
Highlights
At the end of each fiscal year, non-life insurance companies face the situation that the earned premiums are known, but not the outstanding loss liabilities
The resulting distribution-free scalar state space model for cumulative payments can be considered as an extension of the chain ladder (CL) method under the assumption that the observations in the upper triangle are based on unobservable states
The idea behind the scalar state space model is a modification of the CL method to get a meaningful state space representation and to use the K ALMAN-filter for calculating the claims reserves, as well as for measuring their precision
Summary
At the end of each fiscal year, non-life insurance companies face the situation that the earned premiums are known, but not the outstanding loss liabilities. The outstanding claims reserves are often a large share of the liability side of the balance sheet, so it is very important for every non-life insurer to handle claims reserving adequately It is not surprising, that over the past 40 years, numerous reserving methods have been developed, since the early 1990s. There are currently 16 research papers in stochastic claims reserving on the topic of state space models and the K ALMAN-filter Most of these state space representations are based on a calendar year approach, i.e., all available observations of one calendar year are stacked into one observation vector. The resulting distribution-free scalar state space model for cumulative payments can be considered as an extension of the chain ladder (CL) method under the assumption that the observations in the upper triangle are based on unobservable states According to this content, the paper is structured as follows.
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