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A guided tour through quadratic hedging approaches

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  • Schweizer, Martin
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    Abstract

    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. --

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    Bibliographic Info

    Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1999,96.

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    Date of creation: 1999
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    Handle: RePEc:zbw:sfb373:199996

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    Related research

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

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    References

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    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. Huyěn Pham & Nizar Touzi, 1996. "Equilibrium State Prices In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(2), pages 215-236.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    4. repec:wop:humbsf:1998-18 is not listed on IDEAS
    5. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    6. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 11(4), pages 385-413.
    7. repec:fth:inseep:9830 is not listed on IDEAS
    8. 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.
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    Cited by:
    1. Moller, Thomas, 2001. "On transformations of actuarial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 281-303, June.
    2. Moreau, Ludovic, 2012. "A contribution in stochastic control applied to finance and insurance," Economics Thesis from University Paris Dauphine, Paris Dauphine University, Paris Dauphine University, number 123456789/10711 edited by Bouchard, Bruno.
    3. Francesca Biagini & Paolo Guasoni & Maurizio Pratelli, 2000. "Mean-Variance Hedging for Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(2), pages 109-123.
    4. Wang, Qizhi & Chidmi, Benaissa, 2009. "Cotton Price Risk Management across Different Countries," 2009 Annual Meeting, January 31-February 3, 2009, Atlanta, Georgia, Southern Agricultural Economics Association 46762, Southern Agricultural Economics Association.

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