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in BUS 3024S - Contingencies by (130 points)

Could you please explain the answer to this question, in particular why it runs from 1 to 9. Surely if you became sick say at time t=0 then you could in theory be paid for the full 10 years if you remained sick, R50 000 between 0 and 1 and then R20 000 for the remains 9 years, between 1 and 10?image image image

1 Answer

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by (1.6k points)

Look at the integral limits as independent of the term meaning that it is just used as a count. So o to 1 does not mean beginning of term to first year of term. It means beginning of getting sick to one year of being sick. Same with the 1-9. It represents one year of being sick all the way to 9 years of being sick. Since you only receive 50000 in the first year of being sick, this needs to be split up into the first year of being sick (0-1) and then the rest of the time being sick which is 1-9 since if the term of the policy is 10 years and you have to be sick at least 1 year to get the reduced annuity, then there are 9 possible years left to receive this given that you got sick at the start. 


E.g. if you get sick in the second year you will receive 50000 for one year and then you will have a maximum of 7 years to receive 20000 if you stay sick until the end of the term. 
by (1.1k points)
edited by
Hi I'm still a bit confused with the question. Doesn't the integral from 1-9 only cover 8 periods where the life can be sick? Also, why is there no dependance on t in the integrals with respect to s, because surely the number of benefit payments a life receives is dependant on the time they become sick?
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