Hedging Contingent Claims with Constrained Portfolios

We employ a stochastic control approach to study the question of hedging contingent claims by portfolios constrained to take values in a given closed, convex subset of $\mathscr{R}^d$. In the framework of our earlier work for utility maximization with constrained portfolios, we extend results of El Karoui and Quenez on incomplete markets and treat the case of different interest rates for borrowing and lending.