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Deterministic Criteria For The Absence And Existence Of Arbitrage In Multi-Dimensional Diffusion Markets

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  • DAVID CRIENS

    (Department of Mathematics, Technical University of Munich, Munich 80333, Germany)

Abstract

We derive deterministic criteria for the existence and nonexistence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the no unbounded profit with bounded risk condition holds, while the classical no free lunch with vanishing risk condition fails.

Suggested Citation

  • David Criens, 2018. "Deterministic Criteria For The Absence And Existence Of Arbitrage In Multi-Dimensional Diffusion Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-41, February.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:01:n:s0219024918500024
    DOI: 10.1142/S0219024918500024
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    Cited by:

    1. Philip Protter & Aditi Dandapani, 2019. "Strict Local Martingales and the Khasminskii test for Explosions," Papers 1903.02383, arXiv.org.
    2. Dandapani, Aditi & Protter, Philip, 2022. "Strict local martingales and the Khasminskii test for explosions," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 716-728.
    3. David Criens & Mikhail Urusov, 2023. "Criteria for the absence of arbitrage in general diffusion markets," Papers 2306.11470, arXiv.org, revised Sep 2024.
    4. David Criens, 2018. "No Arbitrage in Continuous Financial Markets," Papers 1809.09588, arXiv.org, revised Feb 2020.

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