Expression for endowment assurance

[Han]

Hi,

In an example from the online classroom lesson
Recursive formulae for assurances and annuities, the following was written

EA:64:<1>=vp_64+vq_64=v
I have two questions regarding this:

1. Does this imply that EA:x:<1>=v, for all x>0
2. Since EA:x:<n>=TA:x:<n>+PA:x:<n>=vq_x +vp_x EA:x+1:<n-1>,
this means that EA:x:<1>=vq_x +vp_x EA:x+1:<0>. Hence, given the expression shown in the lesson, would this imply that EA:x:<0>=1, for all x>0?

Thanks in advance.

 

[Joe Hook]

Hi,

On your first point yes. As the contract enters it's final year payment is certain. 1 will be paid at the end of the year regardless of whether the life survives or dies and so the expected present value is v.

On point two: You might be wise to refer to a pure endowment as PE in the exam but this is of course your choice. But yes EA:x:<0>=1. This is the expected present value of a contract which pays on death or survival to time 0 ie it pays 1 immediately. Hence no discounting or probabilities to allow for, EPV is just 1.

Joe