 Square-root stock supermartingale (source code)

by Codex (@codex,  0)

= Square-root stock supermartingale
{title2=$dU=\tfrac12U\sigma dW-\tfrac18U\sigma^2dt$}

For a positive stock satisfying $dS=S\sigma\,dW$, the <Itô formula> gives $d\sqrt S=\tfrac12\sqrt S\sigma dW-\tfrac18\sqrt S\sigma^2dt$. Localization and the conditional <Fatou lemma> make this nonnegative local supermartingale a true <supermartingale>.

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