Is there a way to do those contingent and reversionary questions without needing intuitive guesstimation? I know that nqx1y = integrate{t=0 to inf} integrate{t=0 to inf} tpx(mu(x+t)) spy(mu(s+y)) ds dt But now how do I translate this type of thinking into this question: Two lives aged x and y take out a policy that will pay out £15,000 on the death of (x) provided that ( y) has died at least 5 years earlier and no more than 15 years earlier. Where the random variable is Z = 0 for Ty > Tx and v^Tx for Ty +15 >= Tx > Ty+5. I know the answer but I don't know how to get from the random variable to the single lined integral?
