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Pricing without no-arbitrage condition in discrete time

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  • Laurence Carassus
  • Emmanuel L'epinette

Abstract

In a discrete time setting, we study the central problem of giving a fair price to some financial product. For several decades, the no-arbitrage conditions and the martingale measures have played a major role for solving this problem. We propose a new approach for estimating the super-replication cost based on convex duality instead of martingale measures duality: The prices are expressed using Fenchel conjugate and bi-conjugate without using any no-arbitrage condition.The super-hedging problem resolution leads endogenously to a weak no-arbitrage condition called Absence of Instantaneous Profit (AIP) under which prices are finite. We study this condition in details, propose several characterizations and compare it to the no-arbitrage condition.

Suggested Citation

  • Laurence Carassus & Emmanuel L'epinette, 2021. "Pricing without no-arbitrage condition in discrete time," Papers 2104.02688, arXiv.org.
    • Handle: RePEc:arx:papers:2104.02688
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    References listed on IDEAS

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    1. Manfred Schäl, 1999. "Martingale Measures and Hedging for Discrete-Time Financial Markets," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 509-528, May.
    2. Martin Herdegen & Martin Schweizer, 2018. "Semi‐efficient valuations and put‐call parity," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1061-1106, October.
    3. 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.
    4. 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.
    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. Yuri Kabanov & Constantinos Kardaras & Shiqi Song, 2016. "No arbitrage of the first kind and local martingale numéraires," Finance and Stochastics, Springer, vol. 20(4), pages 1097-1108, October.
    7. Johannes Ruf, 2013. "Negative call prices," Annals of Finance, Springer, vol. 9(4), pages 787-794, November.
    8. repec:dau:papers:123456789/12268 is not listed on IDEAS
    9. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    10. 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.
    11. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
    12. Romain Blanchard & Laurence Carassus, 2018. "Multiple-Priors Optimal Investment In Discrete Time For Unbounded Utility Function," Working Papers hal-01883787, HAL.
    13. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    14. Kabanov, Yuri & Lépinette, Emmanuel, 2013. "Essential supremum with respect to a random partial order," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 478-487.
    15. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    16. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    17. Johannes Ruf, 2012. "Negative Call Prices," Papers 1204.1903, arXiv.org, revised Jan 2013.
    18. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
    19. Claudio Fontana, 2015. "Weak And Strong No-Arbitrage Conditions For Continuous Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-34.
    20. repec:dau:papers:123456789/9699 is not listed on IDEAS
    21. Kabanov, Yuri & Lépinette, Emmanuel, 2013. "Essential supremum and essential maximum with respect to random preference relations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 488-495.
    22. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    23. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
    24. Mathias Beiglbock & Marcel Nutz, 2014. "Martingale Inequalities and Deterministic Counterparts," Papers 1401.4698, arXiv.org, revised Oct 2014.
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    Cited by:

    1. Dorsaf Cherif & Emmanuel Lépinette, 2023. "No-arbitrage conditions and pricing from discrete-time to continuous-time strategies," Post-Print hal-03284660, HAL.
    2. Meriam El Mansour & Emmanuel Lepinette, 2023. "Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty," Papers 2311.08847, arXiv.org.
    3. repec:hal:wpaper:hal-03284660 is not listed on IDEAS

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