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Criteria for NUPBR, NFLVR and the existence of EMMs in integrated diffusion markets

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  • David Criens
  • Mikhail Urusov

Abstract

Consider a single asset financial market whose discounted asset price process is a stochastic integral with respect to a continuous regular strong Markov semimartingale (a so-called general diffusion semimartingale) that is parameterized by a scale function and a speed measure. In a previous paper, we established a characterization of the no free lunch with vanishing risk (NFLVR) condition for a canonical framework of such a financial market in terms of the scale function and the speed measure. Ioannis Karatzas (personal communication) asked us whether it is also possible to prove a characterization for the weaker no unbounded profit with bounded risk (NUPBR) condition, which is the main question we treat in this paper. Here, we do not restrict our attention to canonical frameworks but we allow a general setup with a general filtration that preserves the strong Markov property. Our main results are precise characterizations of NUPBR and NFLVR which only depend on the scale function and the speed measure. In particular, we prove that NUPBR forces the scale function to be continuously differentiable with absolutely continuous derivative. The latter extends our previous result, that, in the canonical framework, NFLVR implies such a property, in two directions (a weaker no-arbitrage notion and a more general framework). We also make the surprising observation that NUPBR and NFLVR are equivalent whenever finite boundary points are accessible for the driving diffusion.

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  • David Criens & Mikhail Urusov, 2023. "Criteria for NUPBR, NFLVR and the existence of EMMs in integrated diffusion markets," Papers 2306.11470, arXiv.org.
    • Handle: RePEc:arx:papers:2306.11470
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    References listed on IDEAS

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    1. Aleksandar Mijatović & Mikhail Urusov, 2012. "Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models," Finance and Stochastics, Springer, vol. 16(2), pages 225-247, April.
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    6. David Criens, 2018. "No Arbitrage in Continuous Financial Markets," Papers 1809.09588, arXiv.org, revised Feb 2020.
    7. Koichiro Takaoka & Martin Schweizer, 2014. "A note on the condition of no unbounded profit with bounded risk," Finance and Stochastics, Springer, vol. 18(2), pages 393-405, April.
    8. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    9. 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.
    10. Constantinos Kardaras & Johannes Ruf, 2020. "Filtration shrinkage, the structure of deflators, and failure of market completeness," Finance and Stochastics, Springer, vol. 24(4), pages 871-901, October.
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    12. Constantinos Kardaras & Johannes Ruf, 2019. "Filtration shrinkage, the structure of deflators, and failure of market completeness," Papers 1912.04652, arXiv.org, revised Aug 2020.
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