The Annals of Applied Probability

Asymptotically optimal discretization of hedging strategies with jumps

Mathieu Rosenbaum and Peter Tankov

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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 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.

Article information

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

Dates
First available in Project Euclid: 23 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1398258094

Digital Object Identifier
doi:10.1214/13-AAP940

Mathematical Reviews number (MathSciNet)
MR3199979

Zentralblatt MATH identifier
1302.91178

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1398258094


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