

\subsection{\bf Stock Market Example of}
\subsection{\bf Multiple Monte Carlos --- I}

\begin{slide}
\begin{itemize}
\item You may think of this as obvious, but let us study its
consequences in a generalized example.  We wish to make money on the
stock market using a Monte Carlo model of their behavior on certain
variables $I=\int f\left( x_1, x_2 \ldots\right)\,dx_1 \ldots$.

\item We need an accuracy of say 1\%.  Then we need a number of events
$n_f$ where $\sigma_f/n_f^{1/2} \sim 0.1 \langle f\rangle$ where
desired integral is up to a constant $\langle f\rangle = \mu_f$.  Then
$$ n_f=10000\left({\sigma_f\over{\mu_f}}\right)^2 $$

\item Now suppose your friend had another set of variables whose Monte
Carlo $J=\int g\left( y_1, y_2, \ldots\right)\,dy_1, dy_2$ required
$$
n_g=10000\left({\sigma_g\over{\mu_g}}\right)^2
$$
\end{itemize}
\end{slide}

