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Expectation Theory

A

Actuary_11

Member
In the Chapter of Mortality Projection
Methods Based on Expectation , page no. 4 , section 1
What is the relationship between alpha_x and f_n,x in Mortality Projection
Like when alpha_x increase , then f_n,x decrease ....and vice versa , so what is the relation between them.
Here we know that alpha_x is the maximum possible reduction in the mortality rate and f_n,x is the total decline expected to be occur in n years .
 
Hi

alpha and f model two different components of the mortality projection:

f is a reduction factor, (eg 5% per annum) so the reduction factor would be 0.95 after one year, 0.95^2 after two years, etc.

The problem with this is that the reduction factor will tend to zero as time increases, which might be too optimistic. To fix this we use the alpha factor to split the reduction factor into a reducing part and a constant part. This means that the reduction factor tends to alpha as t increases. We might choose alpha to be something like 60% if we feel like this is the maximum possible reduction in mortality for this particular cause.

Hope that helps

Dave
 
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