Pathwise no-arbitrage in a class of Delta hedging strategies  

作　　者：Alexander Schied Iryna Voloshchenko 

机构地区：[1]I.Voloshchenko Department of Mathematics,University of Mannheim,68131 Mannheim,Germany

出　　处：《Probability, Uncertainty and Quantitative Risk》2016年第1期61-85,共25页概率、不确定性与定量风险（英文）

基　　金：support by Deutsche Forschungsgemeinschaft through the Research Training Group RTG 1953.

摘　　要：We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.

关 键 词：Pathwise hedging Exotic options Pathwise arbitrage Pathwise Ito calculus Follmer integral Local volatility Functional Ito formula Functional Cauchy problem on path space 

分 类 号：O17[理学—数学]