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The fundamental theorem of asset pricing under transaction costs


  • Paolo Guasoni


  • Emmanuel Lépinette


  • Miklós Rásonyi



This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes. The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, which reflects future liquidation opportunities. The RNFLVR condition implies that admissible strategies are predictable processes of finite variation. The Appendix develops an extension of the familiar Stieltjes integral for càdlàg integrands and finite-variation integrators, which is central to modelling transaction costs with discontinuous prices. Copyright Springer-Verlag 2012

Suggested Citation

  • Paolo Guasoni & Emmanuel Lépinette & Miklós Rásonyi, 2012. "The fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 16(4), pages 741-777, October.
  • Handle: RePEc:spr:finsto:v:16:y:2012:i:4:p:741-777
    DOI: 10.1007/s00780-012-0185-0

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    References listed on IDEAS

    1. Luciano Campi & Walter Schachermayer, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Finance and Stochastics, Springer, vol. 10(4), pages 579-596, December.
    2. 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.
    3. W. Schachermayer, 1994. "Martingale Measures For Discrete-Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55.
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    5. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
    6. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    7. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    8. repec:crs:wpaper:9513 is not listed on IDEAS
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
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    Cited by:

    1. Bruno Bouchard & Emmanuel Lepinette & Erik Taflin, 2013. "Robust no-free lunch with vanishing risk, a continuum of assets and proportional transaction costs," Papers 1302.0361,
    2. Erindi Allaj, 2013. "Implicit transaction costs and the fundamental theorems of asset pricing," Papers 1310.1882,, revised Jul 2017.
    3. Irene Klein & Emmanuel Lépinette & Lavinia Perez-Ostafe, 2014. "Asymptotic arbitrage with small transaction costs," Finance and Stochastics, Springer, vol. 18(4), pages 917-939, October.
    4. Takaki Hayashi & Yuta Koike, 2017. "No arbitrage and lead-lag relationships," Papers 1712.09854,
    5. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    6. Paolo Guasoni & Mikl'os R'asonyi, 2015. "Hedging, arbitrage and optimality with superlinear frictions," Papers 1506.05895,
    7. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    8. repec:wsi:ijtafx:v:20:y:2017:i:04:n:s0219024917500248 is not listed on IDEAS
    9. Przemys{l}aw Rola, 2014. "Arbitrage in markets with bid-ask spreads," Papers 1407.3372,
    10. repec:pal:assmgt:v:17:y:2016:i:2:d:10.1057_jam.2015.42 is not listed on IDEAS
    11. Xiang Yu, 2014. "Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments," Papers 1408.1382,, revised Jul 2016.
    12. Giuseppe Benedetti & Luciano Campi, 2011. "Multivariate utility maximization with proportional transaction costs and random endowment," Working Papers hal-00586377, HAL.
    13. Adrien Nguyen Huu, 2011. "A note on super-hedging for investor-producers," Papers 1112.4740,, revised Mar 2012.
    14. repec:eee:spapps:v:127:y:2017:i:10:p:3331-3353 is not listed on IDEAS
    15. Tomasz R. Bielecki & Igor Cialenco & Rodrigo Rodriguez, 2012. "No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs," Papers 1205.6254,, revised Jun 2013.
    16. Erhan Bayraktar & Xiang Yu, 2013. "On the Market Viability under Proportional Transaction Costs," Papers 1312.3917,, revised Jan 2017.
    17. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.

    More about this item


    Arbitrage; Fundamental theorem of asset pricing; Transaction costs; Admissible strategies; Finite variation; 91B28; 62P05; 26A45; 60H05; G12;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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