Finance and stochastics vol:9 issue:1 pages:109-127
Except for the geometric Brownian model and the geometric Poissonian model, the general geometric Levy 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 Levy 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.