I think the integral will converge when we use bounded scoring rules. The integral can be rewritten to have its integration limits finite with probability one, as it in practice integrates from 0 to the event time T, which should be assumed to be finite with probability 1. (The score is 0 from T to ∞, since p(t) equals the outcome at any time after T. I might not have been sufficiently clear about that though.)
Thank you!
I think the integral will converge when we use bounded scoring rules. The integral can be rewritten to have its integration limits finite with probability one, as it in practice integrates from 0 to the event time T, which should be assumed to be finite with probability 1. (The score is 0 from T to ∞, since p(t) equals the outcome at any time after T. I might not have been sufficiently clear about that though.)