Originally Posted by Actuarial Guru
The following is a sentence from SOA 67.
"The policy will pay 1000 for each day, up to 2 days, that the opening game is postponed."
To me this sounds like the policy will pay 1000 on the first day it rains and then 2000 on the second day it rains and after that, the policy will not pay anything regardless of whether or not it rains.
What they really meant to say was that the policy will pay 2000 for each day after and including day 2, that it rains.
How come they couldn't have just stated that the policy pays 1000 for the first day that it doesn't rain and 2000, for each day after ?
That's not at all what they mean. Suppose that the opening game is originally scheduled for April 1. What they mean is that if there is no rain and the game is played on April 1, there is no payment. If it rains on April 1 but not April 2, then there is a payment of 1,000.
If it rains on April 1 and April 2, then the payment is 1,000 for April 1, and 1,000 for April 2, for a total of 2,000. Note that the payment for April 2 is still 1,000 -- the point is that if N=2, we have 2 payments of 1,000 which is why the total payment is 2,000.
If it rains on April 1, 2, 3, 4, and 5, then there is a payment of 1,000 for April 1, another 1,000 for April 2, and then we have hit the limit so there is no payment on April 3, 4 or 5. The total payment when N=5 (or anything else >=2) is still 2,000 because there are still the 2 payments of 1,000 (one on April 1 and a second on April 2).
If they paid 2,000 for each day after, and including day 2 for which it rains, then 5 days of rain results in a payment of 1,000 (for day 1) + 2,000 (for day 2) + 2,000 (for day 3) + 2,000 (for day 4) + 2,000 (for day 5) = 9,000 total, which isn't what they are using.