Asymptotically optimal discretization of hedging strategies with jumps

Mathieu Rosenbaum and Peter Tankov

Papers from arXiv.org

Abstract: 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.

Date: 2011-08, Revised 2014-04
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Citations: View citations in EconPapers (14)

Published in Annals of Applied Probability 2014, Vol. 24, No. 3, 1002-1048

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