CT-5 Commutation Function

[Sunil Sanga]

While using commutation we define anuuity - sometimes āx and sometimes ax
For example Question April 2005 - Question 8

In this question in both PSL and FSL (ax) is used, however in question OCT 2011 Question 11 (āx) is used.

Doubts:-

A) What is significance of using these Two different notations in similar questions
B) While deriving what all assumption we need to take care

Regards
Sunil

 

[deepakraomore]

A) No significance. Since whatever notation you used, needs to define properly.
Means if you use \(\bar a_x\) or \(a_x\) or say (by)
Define it as "it is EPV of pension or annuity of unit(1) pa payable to person who just retired at age x+0.5 as per the scheme ..."
In the chapter it is mentioned that you can define and interpret the notations you used.
B) Basic thing to care about is the subscripts and powers. for example -
i) Expected number of person retiring or leaving \(d_x\) or \(i_x\); not \(d_{x+0.5}\) or \(i_{x+0.5}\)
ii) we always assume that payments are made halfway so \(v^{x+0.5}\)
iii) There is difference in commutation function \(C\) defined for fixed benefit and salary related benefit
for fixed benefit \(C^r_x\)
for salary related benefit \(^sC^{ra}_{x+0.5}\)

 

[Sunil Sanga]

Thanks