Insiders and their Free Lunches: the Role of Short Positions

TL;DR

This paper investigates insider arbitrage opportunities under short-selling restrictions by introducing the minimal supermartingale measure and analyzing its properties, revealing conditions where insider advantage may exist due to perceived null events.

Contribution

It introduces the concept of minimal supermartingale measure and explores its relationship with the minimal martingale measure, especially in cases where they fail to exist, impacting insider trading strategies.

Findings

Conditions where both measures fail to exist

Insider advantage linked to perceived null events

Implications for local risk-minimisation strategies

Abstract

Given a stock price process, we analyse the potential of arbitrage by insiders in a context of short-selling prohibitions. We introduce the notion of minimal supermartingale measure, and we analyse its properties in connection to the minimal martingale measure. In particular, we establish conditions when both fail to exist. These correspond to the case when the insider's information set includes some non null events that are perceived as having null probabilities by the uninformed market investors. These results may have different applications, such as in problems related to the local risk-minimisation for insiders whenever strategies are implemented without short selling.