Q&A part 3 q3.29

I'm having trouble with the following question.

Two lives aged x and y take out a policy that will pay out £15 000 on death of (x) provided that (y) has died at least 5 years earlier and no more than 15 years earlier.

(i) Express the PV of this benefit in terms of random variables denoting future lifetimes of (x) and (y)

 

Do it this way make y die at a point t where the range of t should be from 0 to infinity , make x die in an integral and range of that integral should be from t+5 to t+15.

(integrate (0 to infinity) v^t*tpy*muy+t) ((integrate (t+5 to t+15) v^(s-t) spx*mux+s)ds))dt

 

Hi Mohit, I still don't get how we get the Present value Tx bounds or the integral expression

 

check this integral

 

that part I understand, how do we get the required interval for which Tx lies in?

 

it means if y dies at point t , then x must die between t+5 to t +15, that means x must survive for at least 5 years
after death of y and then x must die within 15 year of death of y.

so that is why x must die between the range of t+5 to t+15.

 

Thank you. My brain couldn't reason it out at all