Levental, Shlomo
[VerfasserIn]
;
Schroder, Mark D.
[Sonstige Person, Familie und Körperschaft];
Sinha, Sumit
[Sonstige Person, Familie und Körperschaft]
A Simple Proof of Functional Itô's Lemma for Semimartingales with an Application
Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments March 27, 2013 erstellt
Beschreibung:
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