Quantifying the value of initial investment information

We consider an investor maximizing his expected utility from terminal wealth with portfolio decisions based on the available information flow. This investor faces the opportunity to acquire some additional initial information G.. The subjective fair value of this information for the investor is defined as the amount of money that he can pay for G such that this cost is balanced out by the informational advantage in terms of maximal expected utility. We calculate this value for common utility functions in the setting of a complete market modeled by general semimartingales. The main tools are results of independent interest, namely a martingale preserving change of measure and a martingale representation theorem for initially enlarged filtrations.