  Motivated by problems in insurance, our task is to predict finite upper
bounds on a future draw from an unknown distribution $p$ over the set of
natural numbers. We can only use past observations generated independently and
identically distributed according to $p$. While $p$ is unknown, it is known to
belong to a given collection ${\cal P}$ of probability distributions on the
natural numbers.
  The support of the distributions $p \in {\cal P}$ may be unbounded, and the
prediction game goes on for \emph{infinitely} many draws. We are allowed to
make observations without predicting upper bounds for some time. But we must,
with probability 1, start and then continue to predict upper bounds after a
finite time irrespective of which $p \in {\cal P}$ governs the data.
  If it is possible, without knowledge of $p$ and for any prescribed confidence
however close to 1, to come up with a sequence of upper bounds that is never
violated over an infinite time window with confidence at least as big as
prescribed, we say the model class ${\cal P}$ is \emph{insurable}.
  We completely characterize the insurability of any class ${\cal P}$ of
distributions over natural numbers by means of a condition on how the
neighborhoods of distributions in ${\cal P}$ should be, one that is both
necessary and sufficient.
