Almost sure optimal hedging strategy

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.

Published in at http://dx.doi.org/10.1214/13-AAP959 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces
• Asymptotically optimal discretization of hedging strategies with jumps

Cited by in corpus (4)

• Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach
• First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations
• Optimal hedging of a perpetual American put with a single trade
• Asymptotic Optimal Tracking: Feedback Strategies