No-arbitrage concepts in topological vector lattices
| Autor: | Eckhard Platen, Stefan Tappe |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Function space
General Mathematics Structure (category theory) Topology 0101 Pure Mathematics 0102 Applied Mathematics 01 natural sciences Measure (mathematics) Theoretical Computer Science FOS: Economics and business 010104 statistics & probability 0502 economics and business FOS: Mathematics 0101 mathematics Mathematics Sequence Numéraire 050208 finance Stochastic process Probability (math.PR) 05 social sciences Fundamental theorem of asset pricing Mathematical Finance (q-fin.MF) Functional Analysis (math.FA) Mathematics - Functional Analysis Quantitative Finance - Mathematical Finance Convex cone Mathematics - Probability Analysis |
| Zdroj: | Positivity. 25:1853-1898 |
| ISSN: | 1572-9281 1385-1292 |
| DOI: | 10.1007/s11117-021-00848-z |
| Popis: | 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 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, NAA$_1$ and NA$_1$ may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a num\'{e}raire, 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. Comment: 35 pages |
| Databáze: | OpenAIRE |
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