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Robust Fundamental Theorem for Continuous Processes

Author

Listed:
  • Sara Biagini

    (University of Pisa - Università di Pisa)

  • Bruno Bouchard

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Constantinos Kardaras

    (LSE - London School of Economics and Political Science)

  • Marcel Nutz

    (Dept. of Mathematics - Columbia University [New York])

Abstract

We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family P of possible physical measures. A robust notion NA1(P) of no-arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first main result is a version of the fundamental theorem of asset pricing: NA1(P) holds if and only if every P ∈ P admits a martingale measure which is equivalent up to a certain lifetime. The second main result provides the existence of optimal superhedging strategies for general contingent claims and a representation of the superhedging price in terms of martingale measures.

Suggested Citation

  • Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    • Handle: RePEc:hal:journl:hal-01076062
    DOI: 10.1111/mafi.12110
    Note: View the original document on HAL open archive server: https://hal.science/hal-01076062
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    References listed on IDEAS

    as
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