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Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 4, Pages 672–691 (Mi tvp2015)  

This article is cited in 11 scientific papers (total in 11 papers)

On the mean-variance hedging problem

A. V. Melnikov, M. L. Nechaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper proposes a new approach to the problem of the “optimal” control assets on an incomplete market. The approach develops the known mean-variance hedging method of Folmer, Sonderman, and Schweizer. Some technical assumptions on the approximating sequence such as the nondegeneracy condition and its elements belonging to the space $\mathscr{L}_2$ are excluded. We give examples and an interpretation of obtained results which connect them with such key financial-market notions as completeness and arbitrage.

Keywords: mean-variance hedging, investment, arbitrage, martingale measure, option.

DOI: https://doi.org/10.4213/tvp2015

Full text: PDF file (2104 kB)

English version:
Theory of Probability and its Applications, 1999, 43:4, 588–603

Bibliographic databases:

Received: 05.05.1997

Citation: A. V. Melnikov, M. L. Nechaev, “On the mean-variance hedging problem”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 672–691; Theory Probab. Appl., 43:4 (1999), 588–603

Citation in format AMSBIB
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\paper On the mean-variance hedging problem
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\pages 672--691
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\zmath{https://zbmath.org/?q=an:0953.60024}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 4
\pages 588--603
\crossref{https://doi.org/10.1137/S0040585X97977136}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Matsumoto K., Shimizu K., “Hedging Derivatives on Two Assets With Model Risk”, Asia-Pac. Financ. Mark.  crossref  isi
    2. A. S. Cherny, “Pricing with coherent risk”, Theory Probab. Appl., 52:3 (2008), 389–415  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. N. S. Demin, A. V. Erlykova, E. A. Panshina, “Issledovanie odnogo vida ekzoticheskikh optsionov pri nalichii ottoka i pritoka kapitala v binomialnoi modeli $(B,S)$-rynka tsennykh bumag”, Diskretn. analiz i issled. oper., 16:6 (2009), 23–42  mathnet  mathscinet  zmath
    4. Wang Yu., “Quantile hedging for guaranteed minimum death benefits”, Insurance Mathematics & Economics, 45:3 (2009), 449–458  crossref  mathscinet  zmath  isi  scopus
    5. Cerny A., Kallsen J., “Hedging by Sequential Regressions Revisited”, Mathematical Finance, 19:4 (2009), 591–617  crossref  mathscinet  zmath  isi  elib  scopus
    6. Matsumoto K., “Dynamic programming and mean-variance hedging with partial execution risk”, Review of Derivatives Research, 12:1 (2009), 29–53  crossref  zmath  isi  scopus
    7. Wang Yu. Yin G., “Quantile Hedging for Guaranteed Minimum Death Benefits with Regime Switching”, Stoch. Anal. Appl., 30:5 (2012), 799–826  crossref  mathscinet  zmath  isi  elib  scopus
    8. Krasii N.P., “O vychislenii spreda dlya obobschënnoi modeli (b,s)-rynka v sluchae skupki aktsii”, Inzhenernyi vestnik dona, 23 (2012), 194–194  elib
    9. Subramanian E., Bhat S.P., “Discrete-Time Quadratic-Optimal Hedging Strategies for European Contingent Claims”, 2015 IEEE Symposium Series on Computational Intelligence (SSCI) (Cape Town, South Africa), IEEE, 2015, 1786–1793  crossref  isi  scopus
    10. Matsumoto K., “Mean-Variance Hedging With Model Risk”, Int. J. Financ. Eng., 4:4 (2017), 1750042  crossref  mathscinet  isi
    11. Augustyniak M., Godin F., Simard C., “Assessing the Effectiveness of Local and Global Quadratic Hedging Under Garch Models”, Quant. Financ., 17:9 (2017), 1305–1318  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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