Anticipative portfolio optimization

We study a classical stochastic control problem arising in financial economics: to maximize expected logarithmic utility from terminal wealth and/or consumption. The novel feature of our work is that the portfoilo is allowed to anticipate the future, i.e. the terminal values of the prices, or of the driving Brownian motion, are known to the investor, either exactly or with some uncertainty. Results on the finiteness of the value of the control problem are obtained in various setups, using techniques from the so-called enlargement of filtrations. When the value of the problem is finite, we compute it explicitly and exhibit an optimal portfolio in closed form.