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A conditional version of the second fundamental theorem of asset pricing in discrete time

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  • Lars Niemann
  • Thorsten Schmidt

Abstract

We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices. Moreover, we characterize attainability and market completeness. We derive a conditional version of the second fundamental theorem of asset pricing, which, surprisingly, is not available up to now. The main tool we use are time consistency properties of dynamic nonlinear expectations, which we apply to the super- and subhedging prices. The results obtained extend existing results in the literature, where the conditional setting is considered in most cases only on finite probability spaces.

Suggested Citation

  • Lars Niemann & Thorsten Schmidt, 2021. "A conditional version of the second fundamental theorem of asset pricing in discrete time," Papers 2102.13574, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2102.13574
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    References listed on IDEAS

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    1. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    2. repec:hum:wpaper:sfb649dp2005-006 is not listed on IDEAS
    3. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
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    Cited by:

    1. Philippe Artzner & Karl‐Theodor Eisele & Thorsten Schmidt, 2024. "Insurance–finance arbitrage," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 739-773, July.

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