Especially at old and young ages and where data is

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Unformatted text preview: ts 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 chi-square 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 Chi-square (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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