  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.
