John, Can you please explain the solution to Q3.12 ( Q&A Bank ). How do they decide on the limits of integration? What do those integrals mean in words? Also what is the integral expression for the EPV of Assurance payable immediately on death of (x) provided that it occurred within 10 years from the death of (y) ? Thank you
Q & A bank 3.12 Hi Richard, One of the main points about these discussion forums is that it gives students a chance to chat to each other about topics with each other. It may be that there is a student out there with a fantastic answer to your question who isn't called John! I am called John so I will answer your question... Let's stumble into this qn blind and write 10q45 10 p 40 15 q 50 v^25 ie 45-yr old dies and 40 year old survives 10 years then 40-yr old dies between ages 50 and 65 and gets paid at time 25. Any good? No! There's loads wrong with it but all the problems come back to the fact that we need to pinpoint the 40 year old's death - hence integral with him dying at EXACT time t. So, integral from 10 to infiinity of tq45 t p 40 m 40+t v^t ie 45 year old dies before time t, 40 yr old survives up until time t and then dies at that exact time, collecting a payment of £1 with PV v^t. Any good? It's very close but there's a problem. We have the 45-yr old dying before time t and yet we need it to be sure that it's no more than 15 years before t. This is guaranteed for t<15 but not when t>15. So, we split the integral into two: integral from 10 to 15 of tq45 t p 40 m 40+t v^t and integral from 15 to infiinity of (tq45 - t-15q45) t p 40 m 40+t v^t The second integral is nearly the same as the first but just makes sure that the 45-yr old doesn't die too early! Good luck! John
Thanks for your answers, John. And sorry I didn't realise that the main point of this forum is to discuss things with other students. I thought it's more about getting help from tutors when you are stuck and other students be able to see the answers in case they have similar questions. Sorry
Point of forum Richard_07, Apologies unnecessary - your presumed reason for this forum is certainly its secondary purpose Good luck! John
