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Quadratic Hedging for Sequential Claims with Random Weights in Discrete Time

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  • Jun Deng
  • Bin Zou

Abstract

We study a quadratic hedging problem for a sequence of contingent claims with random weights in discrete time. We obtain the optimal hedging strategy explicitly in a recursive representation, without imposing the non-degeneracy (ND) condition on the model and square integrability on hedging strategies. We relate the general results to hedging under random horizon and fair pricing in the quadratic sense. We illustrate the significance of our results in an example in which the ND condition fails.

Suggested Citation

  • Jun Deng & Bin Zou, 2020. "Quadratic Hedging for Sequential Claims with Random Weights in Discrete Time," Papers 2005.06015, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:2005.06015
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Tim Leung & Matthew Lorig, 2016. "Optimal static quadratic hedging," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1341-1355, September.
    3. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2018. "No-arbitrage under a class of honest times," Finance and Stochastics, Springer, vol. 22(1), pages 127-159, January.
    4. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2017. "No-arbitrage up to random horizon for quasi-left-continuous models," Finance and Stochastics, Springer, vol. 21(4), pages 1103-1139, October.
    5. Jouini,E. & Cvitanic,J. & Musiela,Marek (ed.), 2001. "Handbooks in Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521792370.
    6. Christoph Frei & Nicholas Westray, 2018. "Optimal execution in Hong Kong given a market-on-close benchmark," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 655-671, April.
    7. Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198.
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