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Mean-variance Hedging in the Discontinuous Case

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  • Jianming Xia

Abstract

The results on the mean-variance hedging problem in Gouri\'eroux, Laurent and Pham (1998), Rheinl\"ander and Schweizer (1997) and Arai (2005) are extended to discontinuous semimartingale models. When the num\'eraire method is used, we only assume the Radon-Nikodym derivative of the variance-optimal signed martingale measure (VSMM) is non-zero almost surely (but may be strictly negative). When discussing the relation between the solutions and the Galtchouk-Kunita-Watanabe decompositions under the VSMM, we only assume the VSMM is equivalent to the reference probability.

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  • Jianming Xia, 2006. "Mean-variance Hedging in the Discontinuous Case," Papers math/0607775, arXiv.org.
    • Handle: RePEc:arx:papers:math/0607775
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    References listed on IDEAS

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    1. Walter Schachermayer, 2005. "A Note On Arbitrage And Closed Convex Cones," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 183-189, January.
    2. 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.
    3. Jianming Xia & Jia‐An Yan, 2006. "Markowitz'S Portfolio Optimization In An Incomplete Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 203-216, January.
    4. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
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