Dynamic Programming and Mean-Variance Hedging in Discrete Time

Applied Mathematical Finance, 2004, 11(1), 1-25

27 Pages Posted: 5 Jul 2004 Last revised: 30 Sep 2019

See all articles by Aleš Černý

Aleš Černý

Cass Business School, City, University of London

Date Written: October 1, 2003

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

Suggested Citation

Černý, Aleš, Dynamic Programming and Mean-Variance Hedging in Discrete Time (October 1, 2003). Applied Mathematical Finance, 2004, 11(1), 1-25. Available at SSRN: https://ssrn.com/abstract=561223 or http://dx.doi.org/10.2139/ssrn.561223

Aleš Černý (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

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