  This paper presents a new framework for Merton's optimal investment problem
which uses the theory of Meyer $\sigma$-fields to allow for signals that
possibly warn the investor about impending jumps. With strategies no longer
predictable, some care has to be taken to properly define wealth dynamics
through stochastic integration. By means of dynamic programming, we solve the
problem explicitly for power utilities. In a case study with Gaussian jumps, we
find, for instance, that an investor may prefer to disinvest completely even
after a mildly positive signal. Our setting also allows us to investigate
whether, given the chance, it is better to improve signal quality or quantity
and how much extra value can be generated from either choice.
