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Arbitrage theory for non convex financial market models

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  • Lepinette, Emmanuel
  • Tran, Tuan

Abstract

We propose a unified approach where a security market is described by a liquidation value process. This allows to extend the frictionless models of the classical theory as well as the recent proportional transaction costs models to a larger class of financial markets with transaction costs including non proportional trading costs. The usual tools from convex analysis however become inadequate to characterize the absence of arbitrage opportunities in non-convex financial market models. The natural question is to which extent the results of the classical arbitrage theory are still valid. Our contribution is a first attempt to characterize the absence of arbitrage opportunities in non convex financial market models.

Suggested Citation

  • Lepinette, Emmanuel & Tran, Tuan, 2017. "Arbitrage theory for non convex financial market models," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3331-3353.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:10:p:3331-3353
    DOI: 10.1016/j.spa.2017.01.011
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    References listed on IDEAS

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    Cited by:

    1. Emmanuel Lépinette & Duc Thinh Vu, 2023. "Dynamic programming principle and computable prices in financial market models with transaction costs," Post-Print hal-03284655, HAL.
    2. Martin Brown & Tomasz Zastawniak, 2019. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Papers 1905.01859, arXiv.org, revised May 2019.
    3. Emmanuel Lépinette & Duc Thinh Vu, 2021. "Dynamic programming principle and computable prices in financial market models with transaction costs," Working Papers hal-03284655, HAL.
    4. Erindi Allaj, 2017. "Implicit Transaction Costs And The Fundamental Theorems Of Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-39, June.
    5. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.

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