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Ito's formula

  1. Jan 19, 2009 #1

    I'm trying to answer this question on why we can apply Ito's formula to the function [tex]F(Z_{t}, S_{t}, B_{t})[/tex] which is a [tex]C^{1,1,2}[/tex] function where:

    [tex]B_{t}[/tex] is standard brownian motion

    [tex]S_{t}=max_{0\leq s\leq t}B_{s}[/tex]
    [tex]Z_{t}= \int_0^t B_{s} ds[/tex]

    I think I basically have to show that [tex]S_{t}[/tex] and [tex]Z_{t}[/tex] are continuous and of bounded variation. But can't quite see how to show either, specially in the case of [tex]S_{t}[/tex] since we know that the standard brownian motion is not of bounded variation.

    any ideas?
  2. jcsd
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