Let (X_{1}, X_{2}, ldots) be independent and identically distributed random variables with (Eleft[X_{i}ight]=0), and let [S_{n}=sum_{i=1}^{n} X_{i}]
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Let \(X_{1}, X_{2}, \ldots\) be independent and identically distributed random variables with \(E\left[X_{i}ight]=0\), and let
\[S_{n}=\sum_{i=1}^{n} X_{i}\]
Show that \(S_{1}, S_{2}, \ldots\) form a martingale
\[E\left[S_{n+1} \mid S_{1}, S_{2}, \ldots, S_{n}ight]=S_{n}\]
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Related Book For
Mathematical Techniques In Finance An Introduction Wiley Finance
ISBN: 9781119838401
1st Edition
Authors: Amir Sadr
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