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Dynamic programming and mean-variance hedging in discrete time

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  • Ales Cerny

Abstract

In this paper the general discrete time mean-variance hedging problem is solved by dynamic programming. Thanks to its simple recursive structure the solution is well suited to computer implementation. On the theoretical side, it is shown how the variance-optimal measure arises in the dynamic programming solution and how one can define conditional expectations under this (generally non-equivalent) measure. The result is then related to the results of previous studies in continuous time.

Suggested Citation

  • Ales Cerny, 2004. "Dynamic programming and mean-variance hedging in discrete time," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 1-25.
    • Handle: RePEc:taf:apmtfi:v:11:y:2004:i:1:p:1-25
    DOI: 10.1080/1350486042000196164
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    Citations

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    Cited by:

    1. Aleš Černý, 2007. "Optimal Continuous‐Time Hedging With Leptokurtic Returns," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 175-203, April.
    2. Koichi Matsumoto, 2009. "Mean-Variance Hedging with Uncertain Trade Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 219-252.
    3. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2012. "Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets," Papers 1205.4089, arXiv.org.
    4. Koichi Matsumoto & Keita Shimizu, 2020. "Hedging Derivatives on Two Assets with Model Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(1), pages 83-95, March.
    5. Augustyniak, Maciej & Godin, Frédéric & Simard, Clarence, 2019. "A profitable modification to global quadratic hedging," Journal of Economic Dynamics and Control, Elsevier, vol. 104(C), pages 111-131.
    6. Jan Kallsen & Arnd Pauwels, 2011. "Variance-Optimal Hedging for Time-Changed Levy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(1), pages 1-28.

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