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A unified framework for robust modelling of financial markets in discrete time

Author

Listed:
  • Jan Obłój

    (University of Oxford)

  • Johannes Wiesel

    (Columbia University)

Abstract

We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in finite discrete time. In particular, we prove a fundamental theorem of asset pricing and a superhedging theorem which encompass the formulations of Bouchard and Nutz [12] and Burzoni et al. [13]. In bringing the two streams of literature together, we examine and compare their many different notions of arbitrage. We also clarify the relation between robust and classical ℙ-specific results. Furthermore, we prove when a superhedging property with respect to the set of martingale measures supported on a set Ω $\Omega $ of paths may be extended to a pathwise superhedging on Ω $\Omega $ without changing the superhedging price.

Suggested Citation

  • Jan Obłój & Johannes Wiesel, 2021. "A unified framework for robust modelling of financial markets in discrete time," Finance and Stochastics, Springer, vol. 25(3), pages 427-468, July.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:3:d:10.1007_s00780-021-00454-7
    DOI: 10.1007/s00780-021-00454-7
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    References listed on IDEAS

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    Cited by:

    1. Mun-Chol Kim & Song-Chol Ryom, 2022. "Pathwise superhedging under proportional transaction costs," Mathematics and Financial Economics, Springer, volume 16, number 4, June.
    2. Romain Blanchard & Laurence Carassus, 2022. "Super-replication prices with multiple-priors in discrete time," Papers 2202.06534, arXiv.org.

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    More about this item

    Keywords

    Robust pricing and hedging; Superhedging; Model-independent arbitrage; Dynamic programming principle;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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