ALMOST SURE OPTIMAL HEDGING STRATEGY

作者：Gobet Emmanuel^*; Landon Nicolas

来源：Annals of Applied Probability, 2014, 24(4): 1652-1690.

DOI：10.1214/13-AAP959

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

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.

• 出版日期2014-8