State Space Models and the K alman -Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing

Nataliya Chukhrova and Arne Johannssen
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Nataliya Chukhrova: Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany
Arne Johannssen: Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany

Risks, 2017, vol. 5, issue 2, 1-23

Abstract: This paper gives a detailed overview of the current state of research in relation to the use of state space models and the K alman -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 K alman -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.

Keywords: state space models; K alman -filter; stochastic claims reserving; outstanding loss liabilities; ultimate loss; prediction uncertainty; chain ladder method (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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