Change of variable formula for local time of continuous semimartingale

TL;DR

This paper extends a formula for the local time of a function of a semimartingale, proving a stronger trajectorial equality and demonstrating its application in mathematical finance.

Contribution

It generalizes a previous representation formula for local time, establishing a pointwise and trajectorial equality, with an application in finance.

Findings

Established a trajectorial equality for local time representation

Generalized the change of variable formula for local time

Applied the result to a problem in mathematical finance

Abstract

In this paper we generalize a representation formula for the local time of a function of a semimartingale due to Coquet and Ouknine \cite{Ouknine} , our formula being a pointwise equality between two processes we show in addition that the equality is in fact trajectorial, finally we give an application in mathematical finance.