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Diferrence between L x and L [x]

M

m_bora

Member
Hi,

Please can anyone provide me an theoretical interpretation to understand the key differrence between L x (no of lives alive at a time aged x) and L [x].
Given especially that L x+n = L [x] +n.

Thanks,
Mahesh.
 
lx is the number of lives alive in a (notional) population at exact age x.

l[x] is the number of lives alive in a (notional) population who have experienced a specific event at age x.

The event experienced in CT5 is usually taken to be medical underwriting at the start of a life insurance policy to check that the policyholder is in reasonable health. It's therefore appropriate to assume that this person should have lighter mortality (less chance of dying) than the average person on the street who has not had a medical check.

The effect expires over time, so using AM92 mortality, l[x]+2 = lx+2. This makes sense since someone having had a medical two years ago doesn't mean they now have better than average health, as much could have happened to them in two years.

Note that the l values relate to notional populations - they are values chosen to enable us to calculate survival and death probabilities easily, as this is what we are really interested in.
 
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