Before revision:  The implied volatility surface \sigma_{\rm BS for arbitrary maturity and strike in the limit \omega^2 T 0 , \sigma_0^2 T \infty at fixed (\omega^2 T)(\sigma_0^2 T) is represented as an extremal problem .
After revision:  The implied volatility surface \sigma_{\rm BS for arbitrary maturity and strike in  0 , \sigma_0^2 T \infty at fixed (\omega^2 T)(\sigma_0^2 T) is represented as an extremal problem .