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Teoriya Veroyatnostei i ee Primeneniya, 2020, Volume 65, Issue 3, Pages 498–520
DOI: https://doi.org/10.4213/tvp5359
(Mi tvp5359)
 

This article is cited in 8 scientific papers (total in 8 papers)

A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting

Ch. Cuchieroab, I. Kleinab, J. Teichmannab

a Vienna University, Vienna
b ETH Zürich, Zürich, Switzerland
Full-text PDF (513 kB) Citations (8)
References:
Abstract: We present a surprisingly simple version of the fundamental theorem of asset pricing (FTAP) for continuous time large financial markets with two filtrations in an Lp-setting for 1p<. This extends the results of Kabanov and Stricker in [“The Dalang–Morton–Willinger theorem under delayed and restricted information,” in In Memoriam: Paul-André Meyer, Springer, 2006, pp. 209–213] to continuous time and to a large financial market setting while, however, still preserving the simplicity of the discrete time setting. On the other hand, it generalizes Stricker's Lp-version of FTAP [Ann. Inst. H. Poincaré Probab. Statist., 26 (1990), pp. 451–460] towards a setting with two filtrations. We do not assume that price processes are semimartingales (and it does not follow due to trading with respect to the smaller filtration) or have any specific path properties. The two filtrations in question can also be completely general, and we do not require admissibility of portfolio wealth processes. We go for a completely general and realistic result, where trading strategies are just predictable with respect to a smaller filtration than the one generated by the price processes. Applications include modeling trading with delayed information, trading on different time grids, dealing with inaccurate price information, and randomization approaches to uncertainty, which will be dealt with elsewhere.
Keywords: fundamental theorem of asset pricing, large financial markets, filtration shrinkage.
Funding agency Grant number
Eidgenösische Technische Hochschule Zürich
Received: 07.10.2018
English version:
Theory of Probability and its Applications, 2020, Volume 65, Issue 3, Pages 388–404
DOI: https://doi.org/10.1137/S0040585X97T990022
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Ch. Cuchiero, I. Klein, J. Teichmann, “A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting”, Teor. Veroyatnost. i Primenen., 65:3 (2020), 498–520; Theory Probab. Appl., 65:3 (2020), 388–404
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v65/i3/p498
  • This publication is cited in the following 8 articles:
    1. Karen Grigorian, Robert A. Jarrow, “Option Pricing in an Incomplete Market”, SSRN Journal, 2024  crossref
    2. THOMAS KRABICHLER, JOSEF TEICHMANN, “THE JARROW AND TURNBULL SETTING REVISITED”, Int. J. Theor. Appl. Finan., 27:03n04 (2024)  crossref
    3. T. Krabichler, J. Teichmann, “A case study for unlocking the potential of deep learning in asset-liability-management”, Front. Artif. Intell., 6 (2023)  crossref
    4. F. Biagini, A. Mazzon, A.-P. Perkkiö, “Optional projection under equivalent local martingale measures”, Finance Stoch., 27:2 (2023), 435–465  crossref  mathscinet
    5. P. Artzner, K.-T. Eisele, T. Schmidt, “Insurance–finance arbitrage”, Mathematical Finance, 2023  crossref
    6. M. El Mansour, E. Lépinette, “Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty”, MathematicS In Action, 11:1 (2022), 193  crossref  mathscinet
    7. S. H. Sababe, M. Yazdi, M. M. Shabani, “Reproducing kernel Hilbert space based on special integrable semimartingales and stochastic integration”, Korean J. Math., 29:3 (2021), 639–647  crossref  mathscinet  isi
    8. Ya. Limmer, T. Meyer-Brandis, “Large platonic markets with delays”, Int. J. Theor. Appl. Financ., 24:08 (2021), 2150043  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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