Completion of a Lévy market by power-jump assets

José Manuel Corcuera (), David Nualart () and Wim Schoutens ()

Finance and Stochastics, 2005, vol. 9, issue 1, 109-127

Abstract: 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. Copyright Springer-Verlag Berlin/Heidelberg 2005

Keywords: Lévy processes; market models; martingales; SDE; variation; arbitrage; complete markets; moment problem; orthogonal polynomials (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s00780-004-0139-2

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