  We consider the problem of portfolio optimization with a correlation
constraint. The framework is the multiperiod stochastic financial market
setting with one tradable stock, stochastic income and a non-tradable index.
The correlation constraint is imposed on the portfolio and the non-tradable
index at some benchmark time horizon. The goal is to maximize portofolio's
expected exponential utility subject to the correlation constraint. Two types
of optimal portfolio strategies are considered: the subgame perfect and the
precommitment ones. We find analytical expressions for the constrained subgame
perfect (CSGP) and the constrained precommitment (CPC) portfolio strategies.
Both these portfolio strategies yield significantly lower risk when compared to
the unconstrained setting, at the cost of a small utility loss. The performance
of the CSGP and CPC portfolio strategies is similar.
