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Arbitrage-free modeling under Knightian Uncertainty

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  • Matteo Burzoni
  • Marco Maggis

Abstract

We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which require neither specific assumptions on the class of priors $\mathcal{P}$ nor on the structure of the state space. Several aspects of modeling under Knightian Uncertainty are considered and analyzed. We show the need for a suitable adaptation of the notion of No Free Lunch with Vanishing Risk and discuss its relation to the choice of an appropriate filtration. In an abstract setup, we show that absence of arbitrage is equivalent to the existence of \emph{approximate} martingale measures sharing the same polar set of $\mathcal{P}$. We then specialize the results to a discrete-time framework in order to obtain true martingale measures.

Suggested Citation

  • Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:1909.04602
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    References listed on IDEAS

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    2. Romain Blanchard & Laurence Carassus, 2022. "Super-replication prices with multiple-priors in discrete time," Papers 2202.06534, arXiv.org.

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