The fundamental theorem of asset pricing for selffinancing portfolios
Abstract
Consider a financial market with nonnegative semimartingales which does not need to have a numéraire. We are interested in the absence of arbitrage in the sense that no selffinancing portfolio gives rise to arbitrage opportunities, where we are allowed to add a savings account to the market. We will prove that in this sense the market is free of arbitrage if and only if there exists an equivalent local martingale deflator which is a multiplicative special semimartingale. In this case, the additional savings account relates to the finite variation part of the multiplicative decomposition of the deflator.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.05575
 Bibcode:
 2020arXiv200505575P
 Keywords:

 Quantitative Finance  Mathematical Finance;
 Mathematics  Probability
 EPrint:
 25 pages