# 2019 Test 2 Q2d - Multiple State Model

69 views

edited

Hi

Why are the bounds of the annuity integrals for the 50k and 20k benefits not dependant on t? Because once you re-write the memo's answer in terms of annuity functions then it's clear that once the person gets sick, he/she gets the full benefit for 10 years (50k in the 1st year and 20k in the remaining years), regardless of when they got sick. So they can get sick at time 9 and still get 10 years worth of benefits beyond age 60. But the question specifies that benefits cease at age 60, so surely the term of the annuities should depend on the time (t) at which the person got sick to ensure that benefits are not paid beyond age 60?

Also, why are the bounds of the 20k annuity from 1 to 9 instead of 1 to 10, since doesn't an integral over 1-9 only cover 8 years of benefits and the maximum benefit period for the 20k payment is 9 years? (If the person gets sick right from the beginning does he not get 50k for 1 year and 20k for the remaining 9 years if he stays sick?)

Thanks

–1 vote
by (670 points)

Hi

by (1.1k points)
edited by

Hi, I saw that before but it still doesn't really answer my question as I'm still confused, so I was hoping for an explanation from a tutor.

For example, how does the memo's answer account for this statement, since the duration of the annuities are not dependant on t (time the life gets sick):

"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."

If you had to rewrite the memo's answer in terms of annuity functions as I did above, if the life gets sick in the second year they will still receive 20000 for the maximum duration as the term of the annuity is fixed. I understand that the annuity bounds are used as a 'count', but surely the maximum count should depend on t, since the benefits cease at age 60?

Also, why are the bounds of the integral relating to the 20k annuity not 1-10 (covering 9 years of benefits) instead of 1-9 (covering 8 years of benefits)?

“…..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. “

Thanks

by (1.1k points)
Hi could I please get an update on this?