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A guided tour through quadratic hedging approaches


  • Schweizer, Martin


This paper gives an overview of results and developments in the area of pricing and hedging contingent claims in an incomplete market by means of a quadratic criterion. We first present the approach of risk-minimization in the case where the underlying discounted price process X is a local martingale. We then discuss the extension to local risk-minimization when X is a semimartingale and explain the relations to the Föllmer-Schweizer decomposition and the minimal martingale measure. Finally we study mean-variance hedging, the variance-optimal martingale measure and the connections to closeness properties of spaces of stochastic integrals.

Suggested Citation

  • Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199996

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    References listed on IDEAS

    1. Rheinländer, Thorsten & Schweizer, Martin, 1997. "On L2-projections on a space of stochastic integrals," SFB 373 Discussion Papers 1997,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    3. Lamberton, Damien & Pham, Huyên & Schweizer, Martin, 1998. "Local risk-minimization under transaction costs," SFB 373 Discussion Papers 1998,18, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Föllmer, H. & Schweizer, M., 1989. "Hedging by Sequential Regression: an Introduction to the Mathematics of Option Trading," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 19(S1), pages 29-42, November.
    5. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
    6. repec:crs:wpaper:9830 is not listed on IDEAS
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Huyěn Pham & Nizar Touzi, 1996. "Equilibrium State Prices In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 215-236.
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    Cited by:

    1. Francesca Biagini & Paolo Guasoni & Maurizio Pratelli, 2000. "Mean-Variance Hedging for Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 109-123.
    2. S. Cawston & L. Vostrikova, 2010. "$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point," Papers 1004.3525,, revised Jun 2011.
    3. Moller, Thomas, 2001. "On transformations of actuarial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 281-303, June.
    4. Thomas Møller, 2001. "Risk-minimizing hedging strategies for insurance payment processes," Finance and Stochastics, Springer, vol. 5(4), pages 419-446.
    5. Moreau, Ludovic, 2012. "A contribution in stochastic control applied to finance and insurance," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/10711 edited by Bouchard, Bruno, March.
    6. Wang, Qizhi & Chidmi, Benaissa, 2009. "Cotton Price Risk Management across Different Countries," 2009 Annual Meeting, January 31-February 3, 2009, Atlanta, Georgia 46762, Southern Agricultural Economics Association.
    7. Arunangshu Biswas & Anindya Goswami & Ludger Overbeck, 2017. "Option Pricing in a Regime Switching Stochastic Volatility Model," Papers 1707.01237,, revised Jan 2018.

    More about this item


    risk-minimization; locally risk-minimizing; mean-variance hedging; minimal martingale measure; variance-optimal martingale measure; Föllmer-Schweizer decomposition; quadratic hedging criteria; incomplete markets;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General


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