GI ROC reserving study - Effectiveness of Reserving Methods Working
Party
In 2008 the General Insurance Reserve Oversight Committee (GI ROC, UK) initiated
a research project on the effectiveness of reserving methods.
Click here
for the Institute of Actuaries UK Working Party webpage about this research
project.
As part of this actuaries were invited to respond to a practical survey
in which they would analyse and forecast one of eight datasets (A-H)
drawn from real company data using any combination of a number of pre-given
standard methods. The procedure was set up in Excel spreadsheets which
were specially designed so that the data was presented in stages corresponding
to annual reports. In the initial stage there was historic data for
six years and only after fully formulating a reserving procedure and
forecasts on the basis of this level of historic experience was the
participating actuary given the following year's data. This continued
for between three and five stages depending on the dataset. The data
in each case consisted of Paid Losses(PL), Incurred Losses (IL) and
Outstandings (OS) a.k.a. Case Reserve Estimates or CREs. There was usually
one or more exposure vectors and in some cases considerable additional
information relating to claim counts and costs at closure. In all cases
a brief verbal description of the line of business was also given.
The exercise was thus designed to approximate the experience of an actuary
working with limited data and having to refine their understanding in stages
as they gained a deeper historic overview of claims developments.
Insureware was very happy to be invited to participate in this exercise,
but since our modelling approach does not work via traditional methods
or development
factors we could not present our results in the interactive Excel spreadsheets
that were originally used.
Accordingly we created heuristic reports on two of the datasets, A and
C, and have structured these reports to follow what we believe to be
the spirit
of
the exercise. We show how we would typically respond at each stage of
the process while in possession of only the data available at that time.
Dataset A eventually runs to five years of data but only provides PL, IL and
OS and one Exposure measure. It is for for a line of business Aeroplane Parts
Liability, about which few actuaries would be expected to possess a great deal
of experience.
Dataset C has only three years ofdata, but provides many more kinds of data
including Numbers of Claims Closed, Number of Claims Settled at Nil, and
Payments for Claims Finalised. It is for a line of business, Employers
Liability, with
which many actuaries may be already quite experienced.
Summaries of the data for sets A and C.
The opening paragraphs of the Insureware report are reproduced below,
click on the link to download the complete PDF.
The Insureware report was co-authored by David Odell (Insureware), Ben Zehnwirth
(Professorial visiting Fellow University of New South Wales and Insureware),
Henk Jan Prins (Chief Actuary Non Life
Fortis Insurance Netherlands), Paul Kedney (Chief Actuary, AEGIS London)
Introduction and Summary
We provide results on two dataset sequences
A and C to illustrate the way we consider
loss reserving issues. In our view sound loss reserving implies
that the actuary does not
select a method (model) a priori, but analyses the data and then
creates models that work
for the data. A good model is characterised by four essential
and integral components of
interest, namely, each of the trends in the development period,
accident period and
calendar period direction as well as the quality of the volatility
about the trend structure. Calendar year trends project in the
other two directions. The triangle is regarded as a
sample path from the fitted probability distributions in each
cell. All model assumptions
are tested and validated by the data.
The analysis of calendar year trends, superimposed or total, in the
historic claims
performance is crucial to properly carry out the forecasting process.
This is because
assumed level of future inflation usually has a major impact on
the forecast ultimate claim
costs. One of the main drawbacks of the classical link ratio techniques
is the fact that
they do not involve analysis and modelling of inflationary trends.
In practise the claims
performance of most Non Life portfolios is characterised by fluctuating
inflationary
trends. The inability of the ratio techniques to cope with this
phenomenon often results in
incorrect and misleading results.
In ICRFS-Plus the forecasting assumptions are explicit; they
may be based on data types
other than paid losses and must be argued for in terms of the
salient features in the past
experience. The identified model forecasts lognormal distributions
for each cell and their correlations. To determine the distribution
of aggregates (of lognormals) by accident year,
calendar year and total reserve we simulate from the correlated
lognormals as there is no analytical distribution for aggregates
of lognormals.
For our analysis we use the so-called Probabilistic Trend Family
(PTF) modelling
framework. PTF type analyses are compared to two models, often
used in the actuarial
world, which (among others) are part of the Extended Link Ratio
Family (ELRF) modelling framework. The initial (default) models in the ELRF
modelling framework
formulate average link ratio methods as regressions (average
trends) through the origin.
These are extended to include an intercept (Murphy) and a constant
trend in each
development period across the accident periods. The only models
we consider in the
ELRF modelling framework is Mack, that is, the regression formulation
of volume
weighted average (chain ladder) link ratios, and the regression
equivalent of arithmetic
average link ratios.
Both modelling frameworks are incorporated in the ICRFS-Plus
software and are
described in the paper “Best
Estimates for Reserves” (Barnett
and Zehnwirth (2000)).
With traditional techniques the parameters
(e.g. average link ratios) are functions of the
data. By contrast, in the PTF modelling framework the model
design as well as the
parameters are a function of the data.
Set A
For this sequence of datasets we illustrate
the PTF modelling framework on the
incremental paid loss development array paying particular
attention to the issues listed
below:
Choice
of exposure vector
-
The model identification
and testing of model assumptions – note that consideration
of diagnostics is an integral
part of the model identification
process
-
Forecast
of distributions for each cell based on
explicit assumptions
-
Updating
and monitoring. The following are features of the data,
and hence
the
model. They are
explained by a calendar year trend (of
zero) remaining stable and assumptions about the
future
remaining
the same.
-
The model
estimated the year before predicts the volatility
(distributions)
of the observations in the current
calendar year
-
Ultimate
mean estimates remain stable on updating
-
Reserves mean
estimates remain stable on updating
-
Base development
parameters “change” on updating
-
The CVs of the forecast distributions
reduce as we update with more
data as a result of parameter uncertainty
reducing
-
The presence of a non-significant
increase in trend between
the last two calendar years
We track the estimated mean ultimate for
each accident year as we proceed through
the
successive datasets and observe a high degree
of consistency in these figures. This
phenomenon is a feature of the data, as the
only change in structure of the model (and
hence the data) on updating is the development
trends in recent development periods. The
calendar year and accident year trend structure
do not change.
By contrast the Mack and arithmetic average
link ratio (regression) methods applied
to
the paid and incurred (cumulative) triangles
have no predictive power, give wildly
differing means, and often give very different
answers on updating. The CVs are
inconsistent by accident year and do not
reduce on updating the triangles-indeed
they
increase. These are features of the methods,
not the data.
We also model the Case Reserve Estimates
(CREs) in the PTF modelling framework
and find that calendar year trend is negative
until the last two years when it becomes
positive.
Yet, calendar year trend in the incremental
paid triangle is always zero. The recent
positive trend in the CREs is probably
due to catch-up. Perhaps the company
was on the
selling block earlier on! The negative
trend in CREs partially explains low
reserves given
by Mack applied to the incurred triangle
in the first few datasets in the sequence.
Set C
In this example we illustrate a different
kind of analysis. The LOB is Employers
Liability
and so we use broad assumptions about
the probable shape of the development
decay for
this line to forecast at each stage
out to an ultimate at twenty-five development
years.
The forecast assumptions then form
the basis for year by year monitoring
of the results
including the Case Reserve Estimates
(or Outstandings). Since there is a
lot of
information with this dataset relating
to claim numbers and closures we consider
the
possibility of modelling in a frequency/severity
framework.
This methodology seems to be behind
some of the counterintuitive CREs.
We find it of
limited promise due in part to the
higher volatilities and correlations
of Closed Claim
Counts and Average Severities. In
particular we see a very nice illustration
of
Greg Taylor’s see saw hypothesis
which says that average severity is inversely
proportional to
closure rate. The closed claim count
triangle has unstable calendar year
trends and
therefore is unpredictable in terms
of future trends, whereas the paid
losses possess a
stable calendar year trend.
The complete paper can be downloaded
as a PDF
document. (in zip format)
|
