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Exposure to risk - type of rate year

A

Avviey

Member
Hello,

I have an query on type of rate year. How can you tell "age at the birthday in the calendar year of death " means "age next birthday at the previous 1 January"? This is given from the answer, I dont know why it means that.
I appreciate it alot if someone can help.
 
Firstly, don't be put off by the death bit. It just means that, if you died this year, your age label would be

age on your birthday this year

Cheery stuff!

But for someone who is still alive, we classify his/her age label as

age on the birthday in the current CY

Using this definition, everyone's age label will change on 1 Jan. So we have a CYRI starting on 1 Jan. If you were drawing a picture of the rate interval, it starts on 1 Jan, so 1 Jan would go at the left-hand end.

Then it's just a case of working out whether it's

age (last or nearest or next) birthday at the previous or coincident 1 January

The age you will be on your birthday in the current CY is your age next birthday at the start of this year. Hence the age label is equivalent to

age next birthday at the previous or coincident 1 Jan

If that's not obvious, try thinking about an example. Suppose you were born on 24 Sept 1980. Then your age label this year would be 2007-1980 = 27. But your 27th birthday isn't until 24th Sept 2007. So back on 1 Jan 2007, 27 isn't your age last birthday or your age nearest birthday. It is your age next birthday.
 
NCD and Force of Transition

Hi,

I have two more questions from Q&A Bank part 5.

First is part i) from Q 5.5 regarding transition matrix of no claim discount system.
I understand that the transition matrix is 5*5 and I understand how to derive the first two rows and the last row, just I dont know why the 3rd and 4th rows become:

(0.3 0 0 0.7 0 )
(0.1 0.2 0 0 0.7)

As if there is exactly one claim was made at the end of the year, a p/holder drops back two levels, but the 3rd low above looks like dropping back three levels and the probability is the sum of 0.1 and 0.2. Can anyone explain this?

The second is part ii) and iii) from Q 5.11.

ii) When calculating K-M estimate, "Durations at 01.01.1998 "are also included, but the period for this mortality investigation period is from 01.01.1998 to 31.12.2003. So why should we include the durations before 01.01.98 of the first two lives?

iii) Estimating the force of matality, how exactly to calculate the central exposed to risk from age 67 to 68 for this particular question? I see the duration line, but I dont know how to get 6 from duration =0 to duration =3m?

Thank you very very much if someone can help. I have thought about them for long, just no clue at all.

Cheers.
 
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