The Annals of Applied Probability

Asymptotically optimal discretization of hedging strategies with jumps

Mathieu Rosenbaum and Peter Tankov

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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 Birkhäuser/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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Ann. Appl. Probab. Volume 24, Number 3 (2014), 1002-1048.

First available in Project Euclid: 23 April 2014

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Primary: 60H05: Stochastic integrals 91G20: Derivative securities

Discretization of stochastic integrals asymptotic optimality hitting times option hedging semimartingales with jumps Blumenthal–Getoor index


Rosenbaum, Mathieu; Tankov, Peter. Asymptotically optimal discretization of hedging strategies with jumps. Ann. Appl. Probab. 24 (2014), no. 3, 1002--1048. doi:10.1214/13-AAP940.

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