A Simple Proof of Functional Itô's Lemma for Semimartingales with an Application
A Simple Proof of Functional Itô's Lemma for Semimartingales with an Application
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DOI：
10.2139/ssrn.2266460
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
S. Levental;Mark Schroder;S. Sinha
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文献类型：
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作者：
S. Levental;Mark Schroder;S. Sinha
伊藤公式最近由Dupire（2009）扩展到连续半鞅的路的泛函，并由Cont和Fournie（2010 a）扩展到RCLL半鞅的路的泛函。与应用于过程的当前值的函数的传统公式相反，这些扩展适用于过程的历史的泛函。通过修改Dupire的设置，我们开发了新的证明连续的情况下，更一般的RCLL的情况下，更简单。我们还研究了最优控制的应用。
The Ito formula was extended recently by Dupire (2009) to functionals of paths of continuous semimartingales, and by Cont and Fournie (2010a) to functionals of paths of RCLL semimartingales. In contrast to the traditional formula that applies to functions of the current value of a process, these extensions apply to functionals of the history of a process. By modifying Dupire’s setup we develop new proofs for both the continuous case and the more general RCLL case that are much simpler. We also examine an application to optimal control.