Dynamic Programming and Mean-Variance Hedging in Discrete Time

Abstract

In this paper we solve the general discrete time mean-variance hedging problem by dynamic programming. Thanks to its simple recursive structure our solution is well suited for computer implementation. On the theoretical side, we show how the variance-optimal measure arises in our dynamic programming solution and how one can define conditional expectations under this (generally non-equivalent) measure. We are then able to relate our result to the results of previous studies in continuous time, namely Rheinlaender and Schweizer (1997), Gourieroux et al. (1998), and Laurent and Pham (1999).