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Some properties of the variance-optimal martingale measure for discontinuous semimartingales

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  • Arai, Takuji

Abstract

We focus on properties of the variance-optimal martingale measure for discontinuous semimartingales. In particular, we give sufficient conditions for the variance-optimal martingale measure to be a probability measure, and for the density process of the variance-optimal martingale measure to satisfy the reverse Hölder inequality, respectively. Moreover, we study relationship with mean-variance hedging.

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  • Arai, Takuji, 2005. "Some properties of the variance-optimal martingale measure for discontinuous semimartingales," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 163-170, September.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:2:p:163-170
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    References listed on IDEAS

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    1. 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.
    2. 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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    Cited by:

    1. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    2. Takuji Arai, 2005. "Some Remarks On Mean-Variance Hedging For Discontinuous Asset Price Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 425-443.
    3. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2009. "Variance Optimal Hedging for continuous time processes with independent increments and applications," Papers 0912.0372, arXiv.org.

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