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Asymptotically optimal discretization of hedging strategies with jumps

  • Mathieu Rosenbaum
  • Peter Tankov

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize the discretization times. More precisely, a discretization rule is said to be optimal if for a given cost function, no strategy has (asymptotically, for large cost) a lower mean square discretization error for a smaller cost. We focus on discretization rules based on hitting times and give explicit expressions for the optimal rules within this class.

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File URL: http://arxiv.org/pdf/1108.5940
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Paper provided by arXiv.org in its series Papers with number 1108.5940.

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Date of creation: Aug 2011
Date of revision: Apr 2014
Publication status: Published in Annals of Applied Probability 2014, Vol. 24, No. 3, 1002-1048
Handle: RePEc:arx:papers:1108.5940
Contact details of provider: Web page: http://arxiv.org/

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  1. Rosenbaum, Mathieu & Tankov, Peter, 2011. "Asymptotic results for time-changed Lévy processes sampled at hitting times," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1607-1632, July.
  2. Mats Brodén & Peter Tankov, 2011. "Tracking Errors From Discrete Hedging In Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 803-837.
  3. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
  4. Ale\v{s} \v{C}ern\'y & Jan Kallsen, 2007. "On the structure of general mean-variance hedging strategies," Papers 0708.1715, arXiv.org.
  5. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
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