ANTICIPATIVE PORTFOLIO OPTIMIZATION

We study a classical stochastic control problem arising in financial e conomics: to maximize expected logarithmic utility from terminal wealt h and/or consumption. The novel feature of our work is that the portfo ilo is allowed to anticipate the future, i.e. the terminal values of t he prices, or of the driving Brownian motion, are known to the investo r, either exactly or with some uncertainty. Results on the finiteness of the value of the control problem are obtained in various setups, us ing 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.