Adjusted mortality Assignment X1 Q12 X2 Q6

[ActStudent]

Hi,

I've got a question about annuity assurance EPVs with adjusted mortality.

In X1 Q12 (iv), we already have the annuity EPV for the annuity, so the assurance EPV is evaluated using the premium conversion formula.

My question is, first, is it possible to evaluate the assurance EPV at 6% interest rate and arrive at the same answer? (I couldn't) Is it best to always work out the annuity and then apply the premium conversion forumla to work out the assurance function?

Second, why is the "delta" in the premium conversion formula ln 1.05, rather than ln 1.06 (the adjusted rate)?

Similarly, X2 Q6 (ii). in the premium conversion formula, 4% was used, not 5%.

Thanks a lot!

 

[omniscientbeing]

You might want to look at the CT5 FAQ, it answers your question.

If you look at the formula for assurances, you'll see why you can't calculate it directly using the adjusted rate and have to use the premium conversion relationship.

Also, you don't use the adjusted rate in the premium conversion relationship because you're only looking at the interest rate, there's no mortality involved when you're using the relationship, so you wouldn't adjust the interest rate. Not sure if that's right, but that's how i think about it

good luck