Free lunch and arbitrage possibilities in a financial market model with aninsider

We consider financial market models based on Wiener space with two agents o n different information levels: a regular agent whose information is contai ned in the natural filtration of the Wiener process W, and an insider who p ossesses some extra information from the beginning of the trading interval, given by a random variable L which contains information from the whole tim e interval. Our main concern are variables L describing the maximum of a pr icing rule. Since for such L the conditional laws given by the smaller know ledge of the regular trader up to fixed times are not absolutely continuous with respect to the law of L, this class of examples cannot be treated by means of the enlargement of filtration techniques as applied so far. We the refore use elements of a Malliavin and Ito calculus for measure-valued rand om variables to give criteria for the preservation of the semimartingale pr operty, the absolute continuity of the conditional laws oft, with respect t o its law, and the absence of arbitrage. The master example, given by sup(t is an element of [0,1])W(i), preserves the semimartingale property, but al lows for free lunch with vanishing risk quite generally. We deduce conditio ns on drift and volatility of price processes, under which we can construct explicit arbitrage strategies. (C) 2001 Elsevier Science B.V. All rights r eserved.