英文标题：
《A Clark-Ocone type formula via Ito calculus and its application to
finance》
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作者：
Takuji Arai and Ryoichi Suzuki
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最新提交年份：
2019
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英文摘要：
An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional expectations of Malliavin derivatives. Our goal is to extend it to random variables which are not Malliavin differentiable. To this end, we make use of Ito\'s formula, instead of Malliavin calculus. As an application to mathematical finance, we shall give an explicit representation of locally risk-minimizing strategy of digital options for exponential Levy models. Since the payoff of digital options is described by an indicator function, we also discuss the Malliavin differentiability of indicator functions with respect to Levy processes.
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中文摘要：
将给出描述为Levy过程函数的随机变量的显式鞅表示。Clark-Ocone定理表明，鞅表示中出现的被积函数是由Malliavin导数的条件期望给出的。我们的目标是将其推广到不可Malliavin微分的随机变量。为此，我们使用伊藤公式，而不是马利亚文微积分。作为数学金融的一个应用，我们将给出指数Levy模型中数字期权局部风险最小化策略的显式表示。由于数字期权的收益是用指标函数来描述的，因此我们还讨论了指标函数相对于Levy过程的Malliavin可微性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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