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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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  • Mathieu Rosenbaum & Peter Tankov, 2011. "Asymptotically optimal discretization of hedging strategies with jumps," Papers 1108.5940,, revised Apr 2014.
  • Handle: RePEc:arx:papers:1108.5940

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    References listed on IDEAS

    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 Brod'en & Peter Tankov, 2010. "Tracking errors from discrete hedging in exponential L\'evy models," Papers 1003.0709,
    3. Alev{s} v{C}ern'y & Jan Kallsen, 2007. "On the Structure of General Mean-Variance Hedging Strategies," Papers 0708.1715,, revised Jul 2017.
    4. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112,
    5. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
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    Cited by:

    1. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    2. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302,, revised May 2017.
    3. Kühn, Christoph & Muhle-Karbe, Johannes, 2015. "Optimal liquidity provision," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2493-2515.
    4. Christoph Kuhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision," Papers 1309.5235,, revised Feb 2015.
    5. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802,, revised Oct 2013.
    6. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    7. Ibrahim Ekren & Ren Liu & Johannes Muhle-Karbe, 2015. "Optimal Rebalancing Frequencies for Multidimensional Portfolios," Papers 1510.05097,, revised Sep 2017.
    8. Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295,
    9. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2015. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," School of Economics Working Papers 2015-17, University of Adelaide, School of Economics.

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