  Consider a financial market with nonnegative semimartingales which does not
need to have a num\'{e}raire. We are interested in the absence of arbitrage in
the sense that no self-financing 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.
