In the context of large financial markets we formulate the notion of "no asymptotic free lunch with vanishing risk" (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets. We work in the general setting of admissible portfolio wealth processes as laid down by Y. Kabanov (1997) under a substantially relaxed concatenation property and adapt the FTAP proof variant obtained in Cuchiero and Teichmann (2014) for the classical small market situation to large financial markets. In the case of countably many assets, our setting includes the large financial market model considered by M. De Donno et al. (2005) and its abstract integration theory. The notion of (NAFLVR) turns out to be an economically meaningful "no arbitrage" condition (in particular not involving weak-*-closures), and, (NAFLVR) is equivalent to the existence of a separating measure. Furthermore we show -- by means of a counterexample -- that the existence of an equivalent separating measure does not lead to an equivalent \sigma-martingale measure, even in a countable large financial market situation.
In the context of large financial markets we formulate the notion of no asymptotic free lunch with vanishing risk (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets. We work in the general setting of admissible portfolio wealth processes as laid down by Y. Kabanov \mbox{%DIFAUXCMD kab:97 under a substantially relaxed concatenation property and adapt the FTAP proof variant obtained in \mbox{%DIFAUXCMD CT:14 for the classical small market situation to large financial markets. In the case of countably many assets, our setting includes the large financial market model considered by M. De Donno et al. \mbox{%DIFAUXCMD DGP:05 and its abstract integration theory. The notion of (NAFLVR) turns out to be an economically meaningful "no arbitrage" condition (in particular not involving weak-*-closures), and, (NAFLVR) is equivalent to the existence of a separating measure. Furthermore we show -- by means of a counterexample -- that the existence of an equivalent separating measure does not lead to an equivalent \sigma-martingale measure, even in a countable large financial market situation.
R
"no asymptotic free lunch with vanishing risk"
no asymptotic free lunch with vanishing risk
R
(1997)
\mbox{%DIFAUXCMD kab:97
R
Cuchiero and Teichmann (2014)
\mbox{%DIFAUXCMD CT:14
R
(2005)
\mbox{%DIFAUXCMD DGP:05