Before revision:  The formula largely extends the scope of validity of the results obtained by several authors in the Brownian setting , designed to give a genuinely stochastic representation of the optimal delta hedge in the context of cross hedging insurance derivatives generalizing the derivative hedge in the Black-Scholes model .
After revision:  The formula largely extends the scope of validity of the results obtained by several authors in the Brownian setting , designed to give a genuinely stochastic representation of the optimal replication in cross hedging insurance derivatives generalizing the derivative hedge in the Black-Scholes model .