Abstract: In this paper we consider the problem of the quantile hedging from the point of view of a better informed agent acting on the market. The additional knowledge of the agent is modelled by a filtration initially enlarged by some random variable. By using equivalent martingale measures introduced in [1] and [2] we solve the problem for the complete case, by extending the results obtained in [4] to the insider context. Finally, we consider the examples with the explicit calculations within the standard Black–Scholes model.

2000 AMS Mathematics Subject Classification: Primary: 60H30; Secondary: 60G44.

Keywords and phrases: Insider trading, quantile hedging, initial enlargement of filtrations, equivalent martingale measure.