Chapter 25. Practice Question 25.5 (i)

[coyn112]

Hi there,

I was wondering how the calculations are done for the expected cost of increase in reserves. It seems the first year is -(probability of surviving year 1 x P), but I can't quite figure out the following years. Perhaps a recursive formula, but the profit is unknown. The formula in Tables pg 37 will give a value without the variable P for the reserves as it uses the sum assured and an annuity ratio so I don't see how that is helpful. Any guidance would be greatly appreciated.
Thanks!

 

[Michael Clarkson]

Hi coyn112,

The reserve is zero at the start and end of contract and P in the years in between:

t	0 (start of year 1)	1 (end of year 1)	2 (end of year 2)	3 (end of year 3)
Reserve	0	P	P	0

The cost of increase in reserve each year is
- { year-end Reserve x probability of staying in force - start-year reserve x (1+i) }

So in year 1 it is
- { P x p60 - 0 }

Year 2 it is
- { P x p61 - P(1.07) }

Year 3 it is
- { 0 - P(1.07) }

If you look up the probabilities in the tables and plug them into the above you should get the answers shown in the solutions.

Hope helpful
Michael