Merton's Optimal Investment Problem with Jump Signals

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