Additional logarithmic utility of an insider

In this paper, we consider a security market in which two investors on di®erent infor-mation levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's portfolio decisions are based on a public information °ow, the in-sider 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 ¯niteness of this additional utility and to show that it is basically given by the entropy of G. Key Words: utility maximization, insider trading, initial enlargement of ¯ltrations, relative entropy, entrop