  This paper studies arbitrage pricing theory in financial markets with
implicit transaction costs. We extend the existing theory to include the more
realistic possibility that the price at which the investors trade is dependent
on the traded volume. The investors in the market always buy at the ask and
sell at the bid price. Implicit transaction costs are composed of two terms,
one is able to capture the bid-ask spread, and the second the price impact.
Moreover, a new definition of a self-financing portfolio is obtained. The
self-financing condition suggests that continuous trading is possible, but is
restricted to predictable trading strategies having c\'adl\'ag
(right-continuous with left limits) and c\'agl\'ad (left-continuous with right
limits) paths of bounded quadratic variation and of finitely many jumps. That
is, c\'adl\'ag and c\'agl\'ad predictable trading strategies of infinite
variation, with finitely many jumps and of finite quadratic variation are
allowed in our setting. Restricting ourselves to c\'agl\'ad predictable trading
strategies, we show that the existence of an equivalent probability measure is
equivalent to the absence of arbitrage opportunities, so that the first
fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the
use of continuous and bounded variation trading strategies can improve the
efficiency of hedging in a market with implicit transaction costs. To better
understand how to apply the theory proposed we provide an example of an
implicit transaction cost economy that is linear and non-linear in the order
size.
