Generating a Target Payoff Distribution with the Cheapest Dynamic Portfolio: an Application to Hedge Fund Replication

Abstract

This paper provides a new method to construct a dynamic optimal portfolio for asset management in a complete market. The method generates a target payoff distribution by the cheapest dynamic trading strategy. It is regarded as an extension of Dybvig (1988a) to continuous-time framework and dynamic portfolio optimization where the dynamic trading strategy is derived analytically by applying Malliavin calculus. As a practical example, the method is applied to hedge fund replication, which extends Kat and Palaro (2005) and Papageorgiou, Remillard and Hocquard (2008) to multiple trading assets with both long and short positions.