Anticipative portfolio optimization under constraints and a higher interest rate for borrowing

We study a stochastic control problem to maximize expected utility from terminal and/or consumption. The novel feature of our work is that the portfolio is allowed to anticipate the future with constraints and a higher interest rate for borrowing. The investor possesses information about the terminal values of the components of the Brownian motion, possibly distorted by 'noise'. We use the technique from the so-called enlargement of filtrations, to model our problem. General existence results are established for optimal portfolio and consumption strategies. Equivalent conditions for optimality are obtained, and explicit solutions leading to feedback formulae are derived for special utility functions and for deterministic coefficients.