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No free lunch for markets with multiple numéraires

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  • Carassus, Laurence

Abstract

We consider a new framework, that of a global market with a finite number of submarkets, where there is a tradable numéraire for each submarket, but no tradable numéraire for the global market. Under a global no arbitrage condition, we show the existence of a common density from which equivalent (local) martingale measures are constructed for each submarket. We also introduce several superreplication prices, depending on the chosen type of hedging: on the global market, on a given submarket or on all submarkets separably. We prove duality results on these prices that allow to assess differences in characteristics between the submarkets, such as liquidity or credit quality. The results are applied in concrete situations, in particular in a Brownian setup.

Suggested Citation

  • Carassus, Laurence, 2023. "No free lunch for markets with multiple numéraires," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    • Handle: RePEc:eee:mateco:v:104:y:2023:i:c:s0304406822001318
    DOI: 10.1016/j.jmateco.2022.102805
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    References listed on IDEAS

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    1. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    2. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    3. W. Schachermayer, 1994. "Martingale Measures For Discrete‐Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55, January.
    4. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. Hens, Thorsten & Jean-Jacques Herings, P. & Predtetchinskii, Arkadi, 2006. "Limits to arbitrage when market participation is restricted," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 556-564, August.
    7. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    8. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    10. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    11. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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