In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's portfolio decisions are based on a public information flow, the insider possesses from the beginning extra information about the outcome of some random variable G, e.g., the future price of a stock. We solve the two optimization problems explicitly and rewrite the insider's additional expected logarithmic utility in terms of a relative entropy. This allows us to provide simple conditions on G for the finiteness of this additional utility and to show that it is basically given by the entropy of G.

Abstract. 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. His subjective fair value of this information 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 study this value for common utility functions in the setting of a complete market modeled by general semimartingales. The main tools are a martingale preserving change of measure and martingale representation results for initially enlarged filtrations.

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