  We consider a setting where in a known future time, a certain continuous
random variable will be realized. There is a public prediction that gradually
converges to its realized value, and an expert that has access to a more
accurate prediction. Our goal is to study {\em when} should the expert reveal
his information, assuming that his reward is based on a logarithmic market
scoring rule (i.e., his reward is proportional to the gain in log-likelihood of
the realized value).
  Our contributions are: (1) we characterize the expert's optimal policy and
show that it is threshold based. (2) we analyze the expert's asymptotic
expected optimal reward and show a tight connection to the Law of the Iterated
Logarithm, and (3) we give an efficient dynamic programming algorithm to
compute the optimal policy.
