Chances for the honest in honest versus insider trading

TL;DR

This paper compares honest and insider traders in a Black-Scholes market, showing that while insiders typically have higher expected utility, honest traders can outperform insiders with positive probability under certain market conditions.

Contribution

It introduces a novel analysis using anticipating stochastic calculus to demonstrate conditions where honest traders can outperform insiders in terms of utility.

Findings

Insiders have higher expected logarithmic utility than honest traders.

Honest traders can achieve higher utility than insiders with positive probability.

The analysis employs a forward integral variant of the Doléans-Dade exponential process.

Abstract

We study a Black-Scholes market with a finite time horizon and two investors: an honest and an insider trader. We analyze it with anticipating stochastic calculus in two steps. First, we recover the classical result on portfolio optimization that shows that the expected logarithmic utility of the insider is strictly greater than that of the honest trader. Then, we prove that, whenever the market is viable, the honest trader can get a higher logarithmic utility, and therefore more wealth, than the insider with a strictly positive probability. Our proof relies on the analysis of a sort of forward integral variant of the Dol\'eans-Dade exponential process. The main financial conclusion is that the logarithmic utility is perhaps too conservative for some insiders.