| Autor: |
Kühn, Christoph, Molitor, Alexander |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Finance Stoch. 23 (2019) 1049-1077 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00780-019-00403-5 |
| Popis: |
In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov, R\'asonyi, and Stricker (2002). The prospective strict no-arbitrage condition is slightly weaker than robust no-arbitrage, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In contrast to the fundamental theorem of asset pricing of Schachermayer (2004), the consistent frictionless prices may lie on the boundary of the bid-ask spread. On the technical level, a crucial difference to Schachermayer (2004) and Kabanov-R\'asonyi-Stricker (2003) is that we prove closedness without having at hand that the null-strategies form a linear space. |
| Databáze: |
arXiv |
| Externí odkaz: |
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