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APPLYING STATE SPACE MODELS TO STOCHASTIC CLAIMS RESERVING

Published online by Cambridge University Press:  24 November 2020

Radek Hendrych Open the ORCID record for Radek Hendrych [Opens in a new window]  and
Tomas Cipra
Radek Hendrych*
Affiliation:
Faculty of Mathematics and Physics Department of Probability and Mathematical Statistics Charles University Prague, Czech Republic E-Mail: hendrych@karlin.mff.cuni.cz
Tomas Cipra
Affiliation:
Faculty of Mathematics and Physics Department of Probability and Mathematical Statistics Charles University Prague, Czech Republic E-Mail: cipra@karlin.mff.cuni.cz
*
E-Mail: hendrych@karlin.mff.cuni.cz
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Abstract

The paper solves the loss reserving problem using Kalman recursions in linear statespace models. In particular, if one orders claims data from run-off triangles to time series with missing observations, then state space formulation can be applied for projections or interpolations of IBNR (Incurred But Not Reported) reserves. Namely, outputs of the corresponding Kalman recursion algorithms for missing or future observations can be taken as the IBNR projections. In particular, by means of such recursive procedures one can perform effectively simulations in order to estimate numerically the distribution of IBNR claims which may be very useful in terms of setting and/or monitoring of prudency level of loss reserves. Moreover, one can generalize this approach to the multivariate case of several dependent run-off triangles for correlated business lines and the outliers in claims data can be also treated effectively in this way. Results of a numerical study for several sets of claims data (univariate and multivariate ones) are presented.

Keywords

Dependent run-off trianglesIBNR projectionsmissing observationsstate space modelstochastic claims reservingC22C32G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 267 - 301
Copyright
© 2020 by Astin Bulletin. All rights reserved

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