Abstract
In this article, we provide an order-form of the First and the Second Fundamental Theorem of Asset Pricing both in the one-period market model for a finite and infinite state-space and in the case of multi-period model for a finite state-space and a finite time-horizon. The space of the financial positions is supposed to be a Banach lattice. We also prove relevant results in the case where the space of the financial positions is not ordered by a lattice cone.
Highlights
The First Fundamental Theorem of Asset Pricing states that the absence of arbitrage for a stochastic process X is equivalent to the existence of an equivalent martingale measure for X
Kountzakis ing and a Super-Replication Theorem in a model-independent framework are both proposed. These theorems are proved in the setting of finite, discrete time and a market consisting of a risky asset S, as well as options written on this risky asset, too
The role of the existence of an unconditional basic sequence in a Banach space is quoted independently from the results provided in [8], as an important condition for the extraction of results concerning FTAP
Summary
The First Fundamental Theorem of Asset Pricing states that the absence of arbitrage for a stochastic process X is equivalent to the existence of an equivalent martingale measure for X. An important difference between the article of Troitsky and ours is that we extend the framework of Definitions so as to include cases of non-discrete time spaces Another one is that we apply these notions in order to provide a new version of the two FTAP, while in [6] an important ordered -space theory of martingales in Banach lattices is developed. The role of the existence of an unconditional basic sequence in a Banach space is quoted independently from the results provided in [8], as an important condition for the extraction of results concerning FTAP This condition is not irrelevant to ([9], Th. 1.1), about Lindelöf Properties of weak topology, but here it mainly concerns the construction of a Strictly Positive Projection. In the paper [10] ideals of L0 (μ ) are used in order to deduce an FTAP-like result ([10], Lem. 1), while our results refer to sublattices
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