Abstract: The hedger position's value alteration is analyzed,and using the dynamic programming method, the multi-period futures dynamic hedging optimal model is set up.At the same time,the dynamic multi-period strategy is derived.The characteristic lies on three aspects.Firstly,the model reflects the effect of hedging trade cost.This solves the problem of the existing hedging strategies ignoring the impact of trade cost,and improves the model(sprecision and accuracy.Secondly,the impact of futures margin is taken in to account.The futures margin's opportunity loss is brought into hedging strategies,which gives a true picture of futures marg in existing opportunity loss without interest return.Thus the model remedies the limitation thatexisting literatures have no regard of the futures margin's opportunity loss.Thirdly,the principle of the maximum return of the hedger is considered.The malpractice that would only consider the price risk and ignore the futures and spots portfolio's profitis solved.This guarantees the model's practicality and utility.

Key words: hedging, multi period hedging, dynamic programming, optimal model, futures