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The Föllmer-Schweizer decomposition: Comparison and description


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  • Choulli, Tahir
  • Vandaele, Nele
  • Vanmaele, Michèle
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    This paper proposes two main contributions concerning the Föllmer-Schweizer decomposition (called hereafter the FS-decomposition). First we completely elaborate the relationship between this decomposition and the Galtchouk-Kunita-Watanabe decomposition under the minimal martingale measure. The difference between these two decompositions is highlighted in a very practical example, and the martingale tools that enhance this difference are illustrated in the semimartingale framework as well. The second main contribution focuses on the description of the FS-decomposition using the predictable characteristics.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 120 (2010)
    Issue (Month): 6 (June)
    Pages: 853-872

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    Handle: RePEc:eee:spapps:v:120:y:2010:i:6:p:853-872

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    Keywords: Minimal martingale measure Galtchouk-Kunita-Watanabe decomposition Follmer-Schweizer decomposition Incomplete markets Local risk-minimization Predictable characteristics;


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    1. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
    2. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    3. Riesner, Martin, 2006. "Hedging life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 599-608, June.
    4. Thorsten Rheinl\"{a}nder & Gallus Steiger, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," Papers math/0610219,
    5. Fred Benth & Thilo Meyer-Brandis, 2005. "The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps," Finance and Stochastics, Springer, vol. 9(4), pages 563-575, October.
    6. Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
    7. Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
    8. David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non-Attainable Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308.
    9. Tahir Choulli & Christophe Stricker, 2006. "More On Minimal Entropy-Hellinger Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 1-19.
    10. Tahir Choulli & Christophe Stricker, 2005. "Minimal Entropy-Hellinger Martingale Measure In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 465-490.
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    Cited by:
    1. Pansera, Jérôme, 2012. "Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 1-11.
    2. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2014. "Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization," Papers 1406.6902,
    3. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.


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