Klüppelberg, Claudia; Severin, M.
(2001):
Prediction of outstanding insurance claims.
Collaborative Research Center 386, Discussion Paper 258

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Abstract
Building reserves for outstanding liabilities is an important issue in the financial statement of any insurance company. In this paper we present a new model for delay in claim settlement and to predict IBNR (incurred but not reported) claims. The modelling is based on a data set of a portfolio of car liability data, which describes the claim settlement of a car insurance portfolio. The data consists of about 5000 realisations of claims, all of which incurred in 1985 and were followed until the end of 1993. In our model, the total claim amount process (S(t))_{t>0} is described by a Poisson shot noise model, i.e. S(t) = ∑_{n=1}^{N(t)} X_n(tT_n), t≥0 where X_1(.), X_2(.),... are i.i.d. copies of the claim settlement process X(.) and the occurence times (T_i)_{i ∈ N} of the consecutive claims are random variables such that N(t) = #{n ∈ N; T_n ≤ t}, t≥0, is a Poisson process, which is assumed to be independent of X(.). The observed times of occurrences of claims are used to specify and to estimate the intensity measure of the Poisson process N(.). Motivated by results of an exploratory data analysis of the portolio under consideration, a hidden Markov model for X(.) is developed. This model is fitted to the data set, parameters are estimated by using an EM algorithm, and prediction of outstanding liabilities is done and compared with the real world outcome.