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On quadratic hedging in continuous time

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  • Huyên Pham

Abstract

We review the main results in the theory of quadratic hedging in a general incomplete model of continuous trading with semimartingale price process. The objective is to hedge contingent claims by using portfolio strategies. We describe two types of criteria: the so-called (local) risk-minimization and the mean-variance approaches. From a mathematical viewpoint, these optimization problems lead to new variants of decomposition theorems in stochastic analysis. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Huyên Pham, 2000. "On quadratic hedging in continuous time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 315-339, April.
  • Handle: RePEc:spr:mathme:v:51:y:2000:i:2:p:315-339
    DOI: 10.1007/s001860050091
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    Citations

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    Cited by:

    1. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 8(1), pages 1-20, February.
    2. Kamil Kladivko & Mihail Zervos, 2017. "Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging," Papers 1710.00897, arXiv.org.
    3. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    4. Okhrati, Ramin & Balbás, Alejandro & Garrido, José, 2014. "Hedging of defaultable claims in a structural model using a locally risk-minimizing approach," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2868-2891.
    5. George Bouzianis & Lane P. Hughston, 2020. "Optimal Hedging in Incomplete Markets," Papers 2006.12989, arXiv.org, revised Sep 2020.
    6. Koichi Matsumoto, 2009. "Mean-Variance Hedging with Uncertain Trade Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 219-252.
    7. Ramin Okhrati & Alejandro Balb'as & Jos'e Garrido, 2015. "Hedging of defaultable claims in a structural model using a locally risk-minimizing approach," Papers 1505.03501, arXiv.org.
    8. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.

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