Let (t>0) be fixed and (theta_{t}=inf left{s leq t mid M_{t}=B_{s} ight}) where (M_{t}=sup _{s leq t}
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Let \(t>0\) be fixed and \(\theta_{t}=\inf \left\{s \leq t \mid M_{t}=B_{s}\right\}\) where \(M_{t}=\sup _{s \leq t} B_{s}\). Prove that
\[\left(M_{t}, \theta_{t}\right) \stackrel{\text { law }}{=}\left(\left|B_{t}\right|, g_{t}\right) \stackrel{\text { law }}{=}\left(L_{t}, g_{t}\right) \text {. }\]
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Mathematical Methods For Financial Markets
ISBN: 9781447125242
1st Edition
Authors: Monique Jeanblanc, Marc Yor, Marc Chesney
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