英文标题：
《Asymptotic Static Hedge via Symmetrization》
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作者：
Jiro Akahori, Flavia Barsotti, Yuri Imamura
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最新提交年份：
2018
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英文摘要：
This paper is a continuation of Akahori-Barsotti-Imamura (2017) and where the authors i) showed that a payment at a random time, which we call timing risk, is decomposed into an integral of static positions of knock-in type barrier options, ii) proposed an iteration of static hedge of a timing risk by regarding the hedging error by a static hedge strategy of Bowie-Carr type with respect to a barrier option as a timing risk, and iii) showed that the error converges to zero by infinitely many times of iteration under a condition on the integrability of a relevant function. Even though many diffusion models including generic 1-dimensional ones satisfy the required condition, a construction of the iterated static hedge that is applicable to any uniformly elliptic diffusions is postponed to the present paper because of its mathematical difficulty. We solve the problem in this paper by relying on the symmetrization, a technique first introduced in Imamura-Ishigaki-Okumura (2014) and generalized in Akahori-Imamura (2014), and also work on parametrix, a classical technique from perturbation theory to construct a fundamental solution of a partial differential equation. Due to a lack of continuity in the diffusion coefficient, however, a careful study of the integrability of the relevant functions is required. The long lines of proof itself could be a contribution to the parametrix analysis.
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中文摘要：
本文是Akahori Barsotti Imamura（2017）的延续，其中作者i）表明，随机时间付款（我们称之为时间风险）被分解为敲入式障碍期权静态头寸的积分，ii）通过将Bowie-Carr型静态对冲策略对障碍期权的对冲误差视为定时风险，提出了定时风险的静态对冲迭代，以及iii）表明在相关函数可积的条件下，误差通过无限多次迭代收敛到零。尽管包括一般一维扩散模型在内的许多扩散模型都满足所需条件，但由于数学上的困难，本文推迟了适用于任何一致椭圆扩散的迭代静态对冲的构造。本文中，我们通过依赖对称化来解决问题，对称化是在Imamura Ishigaki Okumura（2014）中首次引入并在Akahori Imamura（2014）中推广的一种技术，同时，我们还研究了parametrix，这是摄动理论中的一种经典技术，用于构造偏微分方程的基本解。然而，由于扩散系数缺乏连续性，需要仔细研究相关函数的可积性。长串的证据本身可能有助于参数分析。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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