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Update README.md
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Autoparallel committed Feb 22, 2024
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Note that $L$ effectively changes as parameters of the trading function change.
To see this, note that the trading function must always satisfy:
$$
\Phi^{-1}\left(\frac{x}{L}\right)+\Phi^{-1}\left(\frac{y}{KL}\right) + \sigma \sqrt{\tau} = 0.
\Phi^{-1}\left(\frac{x}{L}\right)+\Phi^{-1}\left(\frac{y}{
\mu L}\right) + \sigma = 0.
$$
For new parameters, $K'$, $\sigma'$ and $\tau'$, we must find an $L'$ so that the trading function is satisfied:
For new parameters $\mu'$ and $\sigma'$ we must find an $L'$ so that the trading function is satisfied:
$$
\Phi^{-1}\left(\frac{x}{L'}\right)+\Phi^{-1}\left(\frac{y}{K'L'}\right) + \sigma' \sqrt{\tau'} = 0.
\Phi^{-1}\left(\frac{x}{L'}\right)+\Phi^{-1}\left(\frac{y}{\mu'L'}\right) + \sigma' = 0.
$$
We can find this new $L'$ using a root finding algorithm.

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