Welcome to the hotseat. We've prepared a guide if you'd like to read more about how it works.

Premium conversion formula

0 votes
asked Nov 8, 2017 in BUS 3024S - Contingencies by anonymous

I know the formula below works


I just want to ask if we do this for any type of whole life product. i.e. does the following hold:

$$\overline{A}_x=1-\delta \overline{a}_x$$


1 Answer

0 votes
answered Nov 11, 2017 by Njabulo.Dube (2,950 points)

Yes, both equations hold. 

A relatively simple proof is to note that for any random variable \(R\), 

$$\ddot{a}_\overline{R|}^{m} = \frac{1-v^{R}}{d^{(m)}} $$

Letting \(R = T_x\), implying that \(m = \infty \), or \(R = K_x^{(m)} + \frac{1}{m} \), and taking the expectation on both the left and right and side of each of the equations yields the desired results respectively.

A more detailed proof can be found on pages 116 and 120 of DHW, \(2^{nd}\) edition.