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The Eﬀect of Duplicate policies
50/72 Actuarial Statistics – Module 8: Method of Graduation
Methods of graduation
Preliminaries The graduation process
1 select a graduation formula 2 estimate the parameter values 3 calculate graduated rates at each age using the ﬁtted
parametric formula
test the goodness of ﬁt of the graduated rates: 4 all the six tests can be used
when using the chisquare test, the number of the degree of
freedom is the number of groups minus the number of
parameters in the graduation formula 50/72 Actuarial Statistics – Module 8: Method of Graduation
Methods of graduation
Preliminaries Other considerations
always check results for reasonableness especially at old and
young ages and where data is scarce
male mortality higher than female
mortality of lives with life insurance policies lower than
population (selection)
mortality of lives who took out life insurance recently lower
than that of lives who took out life insurance a long time ago Financial risks: always consider where the ﬁnancial risks lie,
e.g. an insurance company
will suﬀer great loss if it underestimates mortality for life
insurance contracts
will suﬀer great loss if it overestimates mortality for pension or
annuity contracts Mortality tables will be used to estimate future mortality, so
need to allow for future trends in mortality  projection of
mortality improvement
51/72 Actuarial Statistics – Module 8: Method of Graduation
Methods of graduation
Graduation by Parametric Formula 1 Introduction
2 Testing smoothness
3 Statistical tests
Preliminaries
Chisquare (χ2 ) test
Standardised Deviations Test
Signs test
Cumulative Deviations Test
Grouping of Signs Test
Serial Correlations Test
4 Methods of graduation
Preliminaries
Graduation by Parametric Formula
Graduation by Reference to a Standard Table
Graphical graduation
Statistical Tests
The Eﬀect of Duplicate policies
52/72 Actuarial Statistics – Module 8: Method of Graduation
Methods of graduation
Graduation by Parametric Formula Graduation by Parametric Formula
The graduation procedure:
1 2 choose a mathematical formula with unknown parameters for
µx or qx
determine the parameter values
1
2
3 Maximise the likelihood
Minimise the sum of the squared standardised deviations
Minimise the weighted least square 3 calculate graduate rates using the ﬁtted parametric formula 4 test graduation When choosing a formula
too many parameters  undergraduation may result (less
smooth)
too few parameters ...
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This document was uploaded on 04/03/2014.
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