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Completion of a Lévy market by power-jump assets

Author

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  • José Manuel Corcuera
  • David Nualart
  • Wim Schoutens

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

Suggested Citation

  • José Manuel Corcuera & David Nualart & Wim Schoutens, 2005. "Completion of a Lévy market by power-jump assets," Finance and Stochastics, Springer, vol. 9(1), pages 109-127, January.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:1:p:109-127
    DOI: 10.1007/s00780-004-0139-2
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    Citations

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    Cited by:

    1. Zbigniew Palmowski & {L}ukasz Stettner & Anna Sulima, 2018. "Optimal portfolio selection in an It\^o-Markov additive market," Papers 1806.03496, arXiv.org.
    2. Jose Corcuera & Joao Guerra, 2010. "Dynamic complex hedging in additive markets," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 1023-1037.
    3. Niu, Liqun, 2008. "Some stability results of optimal investment in a simple Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 445-452, February.
    4. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Pricing and hedging contingent claims using variance and higher order moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 531-550, April.
    5. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.
    6. Wing Yan Yip & Sofia Olhede & David Stephens, 2008. "Hedging strategies and minimal variance portfolios for European and exotic options in a Levy market," Papers 0801.4941, arXiv.org, revised Oct 2008.
    7. Sulima Anna, 2021. "The Absence of Arbitrage on the Complete Black-Scholes-Merton Regime-Switching Lévy Market," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(3), pages 72-84, September.

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