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Chapter 21
- Thread starter kimiko
- Start date
Hi Kimiko
If we ignore the Dx/Dx+t term, then the formula is giving us a present value for all the policies in the force at the start of the contract. But the retrospective reserve is the accumulated value per policy in force at the current time.
So we need to accumulate with interest (1+i)^t and divide the assets for the initial number of lives l_x between the survivors l_x+t.
D_x = l_x v^x
So
Dx / Dx+t = (l_x / l_x+t) ( v_x / v_x+t) = (l_x / l_x+t) (1+i)^t
which accumulates the payments and allows for the sharing between the survivors as required.
Best wishes
Mark
Thank you, Mark. Can you kindly help me understand this in the solution to Practice Question 21.3(iii): "Finally, these problems may be made worse if there are more surrenders caused by the increase in interest rates eg because of inability to keep up premiums in a situation of economic recession." Does a increase in interest rates mean economic recession?
Increased interest rates will mean less consumer spending which may cause a recession.
Yes
