基于Malliavin演算的可加过程均值-方差套期保值的封闭表示
A closed-form representation of mean-variance hedging for additive processes via Malliavin calculus
摘要：
研究资产价格服从指数可加过程的均值-方差套期保值问题。跳跃型模型的均值-方差套期保值策略的一些表示已经被提出，但没有一个适合于发展任何给定时间直到成熟期的策略值的数值方法。在本文中，我们的目标是获得一个新的显式封闭形式的表示，这使我们能够开发一个有效的数值方法，使用快速傅立叶变换。注意，我们的表示是用Malliavin导数来描述的。此外，我们说明了指数Lévy模型的数值结果。
英文摘要：
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.
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