A Simple Proof of Functional Itô's Lemma for Semimartingales with an Application

14 Pages Posted: 19 May 2013

See all articles by Shlomo Levental

Shlomo Levental

Michigan State University

Mark D. Schroder

Michigan State University - The Eli Broad Graduate School of Management

Sumit Sinha

Michigan State University

Date Written: March 27, 2013

Abstract

The Itô formula was extended recently by Dupire (2009) to functionals of paths of continuous semimartingales, and by Cont and Fournié (2010) 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.

Keywords: functional Ito

JEL Classification: C00

Suggested Citation

Levental, Shlomo and Schroder, Mark D. and Sinha, Sumit, A Simple Proof of Functional Itô's Lemma for Semimartingales with an Application (March 27, 2013). Available at SSRN: https://ssrn.com/abstract=2266460 or http://dx.doi.org/10.2139/ssrn.2266460

Shlomo Levental (Contact Author)

Michigan State University ( email )

Agriculture Hall
East Lansing, MI 48824-1122
United States

Mark D. Schroder

Michigan State University - The Eli Broad Graduate School of Management ( email )

323 Eppley Center
East Lansing, MI 48824-1121
United States
517-432-0622 (Phone)
517-432-1080 (Fax)

Sumit Sinha

Michigan State University ( email )

Agriculture Hall
East Lansing, MI 48824-1122
United States

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