A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements

Abstract

This paper examines optimal consumption and investment choices and the cost of hedging contingent claims in the presence of margin requirements or, more generally, of nonlinear wealth dynamics and constraints on the portfolio policies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities? price process and the investor?s preferences. As an illustration, explicit solutions are provided for an agent with logarithmic utility. A PDE characterization of the cost of hedging a nonnegative path-independent European contingent claim is also provided.