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Robust martingale selection problem and its connections to the no‐arbitrage theory

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  • Matteo Burzoni
  • Mario Šikić

Abstract

We analyze the martingale selection problem of Rokhlin in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no‐arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in models spanning frictionless markets, models with proportional transaction costs, and models for illiquid markets. In all these models, we also incorporate trading constraints.

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  • Matteo Burzoni & Mario Šikić, 2020. "Robust martingale selection problem and its connections to the no‐arbitrage theory," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 260-286, January.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:1:p:260-286
    DOI: 10.1111/mafi.12225
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    Cited by:

    1. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    2. Shuoqing Deng & Xiaolu Tan & Xiang Yu, 2020. "Utility Maximization with Proportional Transaction Costs Under Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1210-1236, November.

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