Insider information and its relation with the arbitrage condition and the utility maximization problem

TL;DR

This paper explores how insider information affects arbitrage opportunities and utility maximization in financial portfolios, showing that insider info does not always lead to arbitrage and analyzing its impact under different utility functions.

Contribution

It provides a detailed analysis of the relationship between insider information, arbitrage conditions, and utility maximization, including explicit examples and bounds.

Findings

Insider information can be bounded even when arbitrage exists.

Insider information does not necessarily imply arbitrage, demonstrated through explicit examples.

The impact of insider information varies with utility functions like logarithmic and CRRA.

Abstract

Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of \emph{insider information}. We assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporary-bankruptcy. In particular, we show that the value of the insider information may be bounded while the arbitrage condition holds and we prove that the insider information does not always imply arbitrage for the insider by providing an explicit example.