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Process for mod of a variable that follows some Stochastic Process

Quantitative Finance Asked by Bogaso on November 28, 2021

Assuming a variable $v$ follows some Stochastic Process as below –

$dv=mu v dt + sigma v dW_t, v in left( -infty, infty right) $

I want to get the process of $|v|$

How can I use the ito's lemma in this context given that the function $|v|$ is not smooth?

One Answer

I think you are looking for extended Ito formula (based on Tanaka's formula).

Bjork's The Pedestrian’s Guide to Local Time should be useful.

Answered by ir7 on November 28, 2021

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