The Annals of Applied Probability

Almost sure optimal hedging strategy

Emmanuel Gobet and Nicolas Landon

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Abstract

In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional Itô model when the discrete rebalancing dates are stopping times. We investigate the convergence, in an almost sure sense, of the renormalized quadratic variation of the hedging error, for which we exhibit an asymptotic lower bound for a large class of stopping time strategies. Moreover, we make explicit a strategy which asymptotically attains this lower bound a.s. Remarkably, the results hold under great generality on the payoff and the model. Our analysis relies on new results enabling us to control a.s. processes, stochastic integrals and related increments.

Article information

Source
Ann. Appl. Probab., Volume 24, Number 4 (2014), 1652-1690.

Dates
First available in Project Euclid: 14 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1400073660

Digital Object Identifier
doi:10.1214/13-AAP959

Mathematical Reviews number (MathSciNet)
MR3211007

Zentralblatt MATH identifier
1298.91165

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60F15: Strong theorems 60H05: Stochastic integrals

Keywords
Almost sure convergence discretization of stochastic integrals option hedging asymptotic optimality

Citation

Gobet, Emmanuel; Landon, Nicolas. Almost sure optimal hedging strategy. Ann. Appl. Probab. 24 (2014), no. 4, 1652--1690. doi:10.1214/13-AAP959. https://projecteuclid.org/euclid.aoap/1400073660


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