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SP7 - UPR question on page 13 of notes

Q

Qayanaat

Member
Can anyone help me with the following question from the course notes:

Premium £3,500. Commission 10%. Started 1 July 2018. Risk starts at zero, increases linearly daily by a constant linear amount over the policy year. Annual policy. Find UPR as at 31st Dec 2018.

How would the answer differ if say policy started 1 August?

Thanks a lot.
 
Don't worry about it until you get to Chapter 15. All will be explained with further methods and examples there.
 
Hi Ian,
Yes I looked at the later chapter where "Uneven Risks" were explained - Page 65 Chapter 15. However, the example used here already specifies that "the risk in first half of the policy is 3 times higher than the risk in second half", so we know already how the risks are allocated over the term of the policy.

What I'm unsure about is how to do the UPR calculation when the question says "increases linearly daily by a constant linear amount". I couldn't see the explanation for this in later chapters (if it's explained in the notes, could you point me to the page and chapter please, I couldn't find any more explanation on this). And also how the answer would differ if we change the start date of the policy. Basically I'm trying to figure out if there's a formula/logic that would work with uneven risks when the risk increases linearly by a constant amount over the term, regardless of the start date of the policy. Can you help please?
 
Let's work in months. If the risk is increasing linearly, then there will be one unit of risk in the first exposed month, 2 in the second, 3 in the third etc, until 12 units in the last month. So if a policy starts on 1 August, there will be 1 in Aug, 2 in Sept, 3 in Oct, 4 in Nov, 5 in Dec. Leaving 6+7+8+9+10+11+12 units unexpired. So UPR will be premium times (6+...+12)/(1+...+12). Does that help?
 
Hi Ian,

Yes that's very clear, thanks very much.
However, applying this logic to the question on page 13 CH, where policy starts 1st July gives:

Total unexpired risks units = 7+8+...+12 = 57
Totat units = 1+2+...+12 = 78
UPR net = 57/78 * 90% premiums = 57/78 * 90% * 3500 = £2301.92

Solution in notes is £2362.50.

My guess is it's probably because we're working in months rather than days maybe, as the question says risk increases linearly daily, would that be correct?
 
Yes - Minh Ho - that's right for the original question in the notes which said the policy incepted on 1 July. Your approach is more accurate than the one used by Qayanaat.
 
Sivapriya K said:
Hi Min Ho, can you please explain it ?
Click to expand...
Simply draw a line start at t=0 and end at t =1 on axis x as time t and axis y as amount of risk.
The amount of risk highest at t = 1 and lowest at t = 0.
The total amount of risk is like the area of the triangle.
Triangle at t =1/2 is 0.25 of triangle at t=1
 
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