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 1≤p<∞. 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.
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
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\paper A~fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting
\jour Teor. Veroyatnost. i Primenen.
\yr 2020
\vol 65
\issue 3
\pages 498--520
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\jour Theory Probab. Appl.
\yr 2020
\vol 65
\issue 3
\pages 388--404
\crossref{https://doi.org/10.1137/S0040585X97T990022}
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Linking options:
https://www.mathnet.ru/eng/tvp5359
https://doi.org/10.4213/tvp5359
https://www.mathnet.ru/eng/tvp/v65/i3/p498
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