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

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 non-linear 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 non-negative path-independent European contingent claim is also provided. Journal of Economic Literature Classification Numbers: D91, D92, G11, G12, C61. ∗We are grateful to Peter Carr, Jaksa Cvitanić and Krishna Ramaswamy for helpful comments.