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Mean-variance hedging and numeraire


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  • Gourieroux, Christian
  • Laurent, Jean-Paul
  • Pham, Huyên


We consider the mean-variance hedging problem when the risky assets price process is a continuous semimartingale. The usual approach deals with self-financed portfolios with respect to the primitive assets family. By adding a numéraire as an asset to trade in, we show how self-financed portfolios may be expressed with respect to this extended assets family, without changing the set of attainable contingent claims. Copyright Blackwell Publishers Inc 1998.

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Bibliographic Info

Paper provided by CEPREMAP in its series CEPREMAP Working Papers (Couverture Orange) with number 9611.

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Length: 23 pages
Date of creation: 1996
Date of revision:
Handle: RePEc:cpm:cepmap:9611

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Cited by:
  1. Dorival Le\~ao & Alberto Ohashi & Vinicius Siqueira, 2013. "A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatility," Papers, 1308.1704,, revised Aug 2013.
  2. Campi, Luciano, 2009. "Mean-Variance Hedging in Large Financial Markets," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/12663, Paris Dauphine University.
  3. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers, 1209.5953,
  4. Liao Wang & Johannes Wissel, 2013. "Mean-variance hedging with oil futures," Finance and Stochastics, Springer, Springer, vol. 17(4), pages 641-683, October.
  5. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series, Oxford Financial Research Centre 2003mf02, Oxford Financial Research Centre.
  6. Frank Thierbach, 2002. "Mean-Variance Hedging under Additional Market Information," Bonn Econ Discussion Papers, University of Bonn, Germany bgse11_2002, University of Bonn, Germany.
  7. Michael Kohlmann & Shanjian Tang, 2000. "Global Adapted Solution of One-Dimensional Backward Stochastic Riccati Equations, with Application to the Mean-Variance Hedging," CoFE Discussion Paper, Center of Finance and Econometrics, University of Konstanz 00-26, Center of Finance and Econometrics, University of Konstanz.
  8. Claudio Fontana, 2013. "Weak and strong no-arbitrage conditions for continuous financial markets," Papers, 1302.7192,, revised May 2014.
  9. Samuel Njoh, 2007. "Cross Hedging Within A Log Mean Reverting Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 887-914.
  10. Kohlmann, Michael & Tang, Shanjian, 2002. "Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 97(2), pages 255-288, February.
  11. Kramkov, D. & Sîrbu, M., 2007. "Asymptotic analysis of utility-based hedging strategies for small number of contingent claims," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 117(11), pages 1606-1620, November.
  12. L. Carassus & E. Temam, 2014. "Pricing and hedging basis risk under no good deal assumption," Annals of Finance, Springer, Springer, vol. 10(1), pages 127-170, February.


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