Completion of a Lévy market by power-jump assets

Except for the geometric Brownian model and the geometric Poissonian model, the general geometric Lévy market models are incomplete models and there are many equivalent martingale measures. In this paper we suggest to enlarge the market by a series of very special assets (power-jump assets) related to the suitably compensated power-jump processes of the underlying Lévy process. By doing this we show that the market can be completed. The very particular choice of the compensators needed to make these processes tradable is delicate. The question in general is related to the moment problem.Received: June 2004, Mathematics Subject Classification (2000): 91B28, 91B26, 91B16, 91B70JEL Classification: C61The work of José Manuel Corcuera and David Nualart is partially supported by the MCyT grant no. BFM200304294. W. Schoutens is a Postdoctoral Fellow of the Fund for Scientific Research - Flanders (Belgium) (F.W.O. - Vlaanderen).