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MODELING

SOURCES:

1. Klugman, S. A., Panjer, H. H., and Willmot, G E. (2004),Loss Models: From Data

to Decisions, 2nd

edition, John Wiley and Sons, New York, Chapter 1.2. Chatfield, C. (2000), Time-Series Forecasting, Chapman & Hall.

Problem in actuarial science:To build a mathematical model which can be used to forecast insurance costs in the

future.

Definition:

A model is a simplified mathematical description which is constructed based on the

knowledge and experience of an analyst combined with data from the past. a model is an approximation to the real phenomenon

Sources of Uncertainties

Three main sources of uncertainties in any mathematical or statistical models:

1. Model uncertainty:

Uncertainty about the structure of the model

Error in the specification of the structure of the model

Error in specifying that the parameters were fixed when they were actually

dependent on time.2. Parameter Uncertainty

Assuming that the model is appropriate, since the parameters are estimated using the

data available, there are uncertainties about the estimates of the parameters.

standard error of the estimators

3. Process Uncertainty

This is an uncertainty about the data, which includes: the unexplained random

variation and measurement and recording errors

There is no such thing as the true modelbecause no model can describe fully the

generating process underlying the data.

There is no such thing as one best model

Modeling process

There are six (6) steps in the process of building mathematical (or probabilistic) models

for a certain real problem:

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1. Model choice

A model isformulated or selectedbased on an analysts: prior knowledge andexperience; and the nature and form of the available data.

2. Model calibrationData are used to calibrate the chosen model; parameter(s) is (are) estimated using the

available data.

3. Model validation

It is important to check whether the fitted model conforms adequately to the data. There

are various diagnostic tests to validate the fitted model, such as: the chi-square goodness-

of-fit test; the Kolmogorov-Smirnov test; qualitative methods.

4. Investigation of other possible models

Even after a suitable model has been found, it is important to investigate if there are other

plausible models. In insurance practice, it is important to consider more than one modelfor a particular problem.

5. Model selection

All valid models are compared using some criteria; this also includes sensitivity analysis

of such models. A model (or maybe more than one model) is selected using previousresults or some other criteria.

6. Model modification for application to the future

The selected models need to be adapted for application to the future. For example, loss orclaims data are very much affected by inflation. Unless this particular variable has been

taken into account in the model, the (parameters of the) selected models need to be

adjusted to forecast the loss in the future.

From time to time, improvements on the model(s) chosen need to be carried out, that is

the six steps above need to be repeated, as more data collected and/or environment (suchas inflation, interest rate, government policy, etc) changes.

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