Prediction of outstanding insurance claims

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(t-T_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.