Introduction
From International Risk Management
Institute, tariff refers to rates and coverages set and published by the rating
party with jurisdiction. The rating party may be moderated, and controlled
either by a company association or a government body. When an insurance company
accepts new insurance or there are changes in the premiums on earlier insurance
due to renewal, the insurance company has to determine the factors that
influence the premiums and calculate the premium according to the values of the
factors. To do that, the company gathers data of the factors that eventually
influence the amount of claims. Few general principles have to be fulfilled
when the company calculates the tariff based on these data; the tariff has to
be as correct as possible in relation to different risk groups. Next, the
structure of tariff along with the calculation of the premium is quite
straightforward. Thus, the factors influencing the tariff have to be few enough
and its structure has to be simple, for example, linear or multiplicative
function of the factors or rather easy to be expressed in tabular form.
Normally, these principles are contradictory; if the premium is correct and
accurate, the structure of the tariff is not simple.
Formulation of
the problem
As claims are contingent, we shall
assume the total amount of claims on a certain risk period as random variable.
To calculate the tariff, we will have to gather both qualitative and
quantitative variables which may have an influence on the amount of claims. For
example, in motor insurance, variables could be area where vehicle is driven,
sex, engine’s stroke capacity, age of vehicle, etc.
1.
The selection problem
From these possible risk variables,
we must select the variables that have significant influence on the amount of claims,
thus we will call them tariff variables or tariff factors. The most difficult
part is choosing and specifying the tariff variables which have the significant
influence and the values.
If the structure of tariff is given,
and the possible tariff variables are quantitative, the tariff variables can
then be determine using the step-wise regression analysis, and it is also
possible to calculate the tariff at the same time. The given tariff structure
also naturally influences the selection of the tariff variables. A better
procedure is try to select the tariff variables without any previous
assumptions about the structure, then the objective is finding the best
construction model, the parameters of which are decided according to several
methods: least squares, Chi-Square minimum, modified Chi-Square and moment
method.
Next, we will look into the degree
of influence in each possible tariff factors. For example, we expect more
accidents will occur in winter than in summer, thus the risk in winter should
be higher than summer, thus seasonality is has high degree of influence here.
Lastly, the selection of tariff
variables is done one by one. For each selection, the influence of the previous
selected variables is taken into consideration. The most difficult part is
measuring the significance of the influence of the different variables.
2.
Tariff construction problem
Here, we have to calculate the
premium as function of tariff variables chosen. To do this, we will first have
to search for tariff factors and then construct the tariff. Research in tariff
theory usually deals with this problem. The most common tariff models are
multiplicative models or sum models.
Risk premium and
collective premium
After the selection problem had been
solved, we can identify risks individually using the value tariff variables and
combine these values together. According to Bühlmann’s practice, we can make
several definitions:
i.
The risk premium is the premium corresponding to
the combination values of the tariff variables and thus defined for each value
combination separately.
ii.
The collective premium is the combine premium with
calculation based on different value combination of the different tariff
factors. In practice, using all of the tariff variables is usually deemed
difficult. Correspondingly, if some of the variables can have many different
values, it is preferable to classify the values into few classes where risks
belonging to a certain class will have the same premium, which is the
collective one. In practice, all insurance premiums can be considered as
collective premiums, because not all tariff variables can be counted as factors
influencing the premium. Thus, the collective premium depends on the
distribution of unused tariff factors where if the distribution of these factors
changed, the collective premium should be adjusted accordingly.
REFERENCE
11. International Risk Management
Institute. Insurance Glossary. Tariff.
Retrieved 19th
22. Paavo Pitkänen (1975). Tariff Theory. ASTIN Bulletin, 8, pp
204-228 doi:10.1017/
S0515036100009338
No comments:
Post a Comment