Chapter 11, Q 11.9

[Avviey]

Hi,

For part 1) of this question, can anyone tell me how this cost of increase in reserves at the end of year 1 - "-0.9920P" calculates? I know the reserve at the beginning of year 1 is zero.

And I have another question, why there isnt an interest earned on reserve component for us to take into account? As the example on page 22 has this component.

Many thanks.

 

[John Potter]

Increase in reserves

The reserve needed per policy at the end of year 1 is P

So, the reserve needed at the end of year 1 per policy in force at the beginning of year 1 is 0.9920P.

Remember that Profit vector is profits at the end of each year per policy in force at the START of THAT year.

John

 

[Avviey]

Hi John,

Thanks for your reply. Yes, the reserve at the end of year 1 is P as the question tells you that reserve is one year's office premium, but I still dont work out where this 0.9920P comes from, as you are not told the reserve percentage?

And the reason that it doesnt require interest earned on reserve is that there is no given experience percentage in the question, otherwise like the example given on page 22, you need to calculate this interest earned on reserve?

Thanks alot again.

 

[John Potter]

Reserves in profit testing

Avviey,

Please read the my post again. Perhaps you missed the second sentence and the words "per policy in force at the beginning of year 1"? ie multiply P by the prob of surviving year 1.

As for interest, the reserves do earn interest but not in year one. There is no reserve at the start of year 1 to earn interest.

In year 2, the reserve at the beginning of the year is P (not 0.9920P because remember that Profit vector is profits at the end of each year per policy in force at the START of THAT year, ie everyone starts year 2 when we're wroking out profit vector) This reserve of P earns interest over the year.

If you have any more trouble perhaps we should sort this out by phone?
01707 275776

John

 

[Avviey]

Hi John,

Finally I get what you meant. Thanks very much. Are the reserve at the begining of the policy term and end of the policy term both zero, eg. Endownment assurance?

And I have one more question of 3.20 on Q&A bank part 3, I dont understand the meaning of d(61) divided by [12 multiplied by l(60)], which is the probability the person dies in 18 months according to the answer.

Thank you very much again.

 

[John Potter]

Q3.20 Q&A bank

Hi Avviey,

When you have a new question, try and get into the habit of posting it as a new query open to everyone. This encourages student discussion and you may get a better answer from a fellow student anyway. I have been snowboarding for the past week so maybe you could have got a quicker answer at the bery least?!

Anyway, withouth looking at the question, it is the prob that a person dies in the 18th month NOT in the next 18 months - does this help?

d61 is the number of people dying between ages 61 and 62. To divide this by 12, you get the number of people dying in any given month between 61 and 62 (assuming UDD, does the qn say this? If not, your answer should).

l60 is the number of people alive age 60 exact.

So, d61/12*l60 is the probability that a life age 60 exact will die in a given month between the ages of 61 and 62. Month 18 is a given month that fits this description.

Good luck!
John