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Risks 2017, 5(2), 30; doi:10.3390/risks5020030

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

Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany
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Academic Editor: Mogens Steffensen
Received: 1 April 2017 / Revised: 7 May 2017 / Accepted: 15 May 2017 / Published: 27 May 2017
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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. View Full-Text
Keywords: state space models; Kalman-filter; stochastic claims reserving; outstanding loss liabilities; ultimate loss; prediction uncertainty; chain ladder method state space models; Kalman-filter; stochastic claims reserving; outstanding loss liabilities; ultimate loss; prediction uncertainty; chain ladder method
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MDPI and ACS Style

Chukhrova, N.; Johannssen, A. State Space Models and the Kalman-Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing. Risks 2017, 5, 30.

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