No-Arbitrage Concepts in Topological Vector Lattices

Eckhard Platen (eckhard.platen@uts.edu.au) and Stefan Tappe

No 410, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition which we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA1 and NA1 may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing. We also consider a nancial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.

Keywords: no-arbitrage concept; topological vector lattice; space of random variables; convex cone (search for similar items in EconPapers)
Pages: 31 pages
Date: 2020-05-01
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Related works:
Working Paper: No-arbitrage concepts in topological vector lattices (2021)
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