标题： 半静态和稀疏方差最优对冲 显示英文标题

标题： Semi-Static and Sparse Variance-Optimal Hedging

摘要： 我们考虑通过由一种资产的动态头寸和其他资产的静态（买入并持有）头寸组成的“半静态”策略来对冲或有要求权。 我们在方差最优性准则下给出了最优策略和对冲误差的一般表示，并在Heston模型情况下使用傅里叶积分提供了可处理的公式。 我们还考虑了最优选择稀疏半静态对冲策略的问题，即仅使用可用对冲资产的一个小子集的策略。 所开发的方法在一个扩展的数值示例中得到说明，其中我们使用欧式期权作为静态对冲资产来计算一个稀疏的半静态对冲。 显示英文摘要

摘要： We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance-optimality and provide tractable formulas using Fourier-integration in case of the Heston model. We also consider the problem of optimally selecting a sparse semi-static hedging strategy, i.e. a strategy which only uses a small subset of available hedging assets. The developed methods are illustrated in an extended numerical example where we compute a sparse semi-static hedge for a variance swap using European options as static hedging assets.