A short note on "Anticipative portfolio optimization"

Abstract

In 1996, Pikovsky and Karatzas did one of the earliest studies on portfolio optimization problems in presence of insider information. They were able to successfully show that the knowledge of the stock price at future time is an insider information with associated unbounded value. However when the insider information only gives an interval containing the future value of the stock price, they could not prove that the value of the information is finite. They made a conjecture of this result and tried to convince about its validity by showing some numerical approximations. Instead of applying more sophisticated results, such as Shannons information theory, we show that their conjecture holds true by giving a simple proof of the finiteness of the value of the insider information for this case.