ALMOST SURE OPTIMAL HEDGING STRATEGY

• 成果类型: Article
• 署名作者: Gobet, Emmanuel; Landon, Nicolas
• 署名单位: Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Engie
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP959
• 发表日期: 2014
• 页码: 1652-1690
• 关键词: convergence; error

摘要

In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional Ito 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 as. processes, stochastic integrals and related increments.