In financial markets, the introduction of inside information can lead to profitable trading opportunities and, in particular, to arbitrage possibilities. In the context of stochastic finance, this issue can be addressed by relying on the theory of enlargement of filtrations. We present some simple examples where informational arbitrage is possible and study the absence of arbitrage under additional information in the context of general semimartingale models. Finally, we try to determine the value of a private information which allows to realize arbitrage opportunities.