  In this paper we present a theoretical framework for determining dynamic ask
and bid prices of derivatives using the theory of dynamic coherent
acceptability indices in discrete time. We prove a version of the First
Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures.
We introduce the dynamic ask and bid prices of a derivative contract in markets
with transaction costs. Based on these results, we derive a representation
theorem for the dynamic bid and ask prices in terms of dynamically consistent
sequence of sets of probability measures and risk-neutral measures. To
illustrate our results, we compute the ask and bid prices of some
path-dependent options using the dynamic Gain-Loss Ratio.
