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).

Keywords: Mean-variance hedging, discrete time, dynamic programming

JEL Classification: G11, G12, C61