  It is shown that delta hedging provides the optimal trading strategy in terms
of minimal required initial capital to replicate a given terminal payoff in a
continuous-time Markovian context. This holds true in market models where no
equivalent local martingale measure exists but only a square-integrable market
price of risk. A new probability measure is constructed, which takes the place
of an equivalent local martingale measure. In order to ensure the existence of
the delta hedge, sufficient conditions are derived for the necessary
differentiability of expectations indexed over the initial market
configuration. The recently often discussed phenomenon of "bubbles" is a
special case of the setting in this paper. Several examples at the end
illustrate the techniques described in this work.
