Another way to get infinite EV in the time of perils model would be to have a nonzero lower bound on the per period risk rate across a rate sequence, but allow that lower bound to vary randomly and get arbitrarily close to 0 across rate sequences. You can basically get a St Petersburg game, with the right kind of distribution over the long-run lower bound per period risk rate. The outcome would have finite value with probability 1, but still infinite EV.
EDIT: To illustrate, if f(r), the expected value of the future conditional on a per period risk rate r in the limit, goes to infinity as r goes to 0, then the expected value of f(r) will be infinite over at least some distributions for r in an interval (0, b], which excludes 0.
Furthermore, if you assign any positive credence to subdistributions over the rates together that give infinite conditional EV, then the unconditional expected value will be infinite (or undefined). So, I think you need to be extremely confident (imo, overconfident) to avoid infinite or undefined expected values under risk neutral expectational total utilitarianism.
Another way to get infinite EV in the time of perils model would be to have a nonzero lower bound on the per period risk rate across a rate sequence, but allow that lower bound to vary randomly and get arbitrarily close to 0 across rate sequences. You can basically get a St Petersburg game, with the right kind of distribution over the long-run lower bound per period risk rate. The outcome would have finite value with probability 1, but still infinite EV.
EDIT: To illustrate, if f(r), the expected value of the future conditional on a per period risk rate r in the limit, goes to infinity as r goes to 0, then the expected value of f(r) will be infinite over at least some distributions for r in an interval (0, b], which excludes 0.
Furthermore, if you assign any positive credence to subdistributions over the rates together that give infinite conditional EV, then the unconditional expected value will be infinite (or undefined). So, I think you need to be extremely confident (imo, overconfident) to avoid infinite or undefined expected values under risk neutral expectational total utilitarianism.