A short note on "Anticipative portfolio optimization"

TL;DR

This paper proves that the value of insider information, which predicts a stock price within an interval, is finite, confirming a conjecture from earlier research using a straightforward proof.

Contribution

The paper provides a simple proof that the value of interval-based insider information in portfolio optimization is finite, confirming a longstanding conjecture.

Findings

Finiteness of insider information value proven for interval predictions

Supports earlier numerical conjectures with a rigorous proof

Simplifies understanding of insider information valuation

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.