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Last survivor annuities

R

Richard_07

Member
Could you please show me how the expected present value of last survivor annuities can be derived.

So how the ∫(bar(at) *fTu(t) )dt can be extended to get to bar(ax)+bar(ay)-bar(ayx)?

Thank you.
 
last survivor annuity integral

Hi Richard,

If we take any two numbers and add the biggest to the smallest then all we have done is add the two numbers up:

min{x,y} + max{x,y} = x + y

The same is true for streams of payments:

a(bar)xy + a(bar)xy(bar) = a(bar)x + a(bar)y *

and for future lifetimes:

Txy + Txy(bar) = Tx + Ty #

This should give you the relationship you want both directly (*) and by manipulating integrals (#)

Good luck!
John
 
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