The seller's risk-indifference price evaluation is studied. We propose a dynamic risk-indifference pricing criterion derived from fully-dynamic risk measures on the $L_p$-spaces for $p\in [1,\infty]$. The concept of fully-dynamic risk measures extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. This family is then characterized by a double time index. Our framework fits well the study of both short- and long-term investments. In this paper we analyze whether the risk-indifference pricing criterion actually provides a proper convex price system. It turns out that, depending on $p$, this is not always the case. Then an extension of the framework beyond $L_p$ becomes necessary. Furthermore, we consider the relationship of the fully-dynamic risk-indifference price with no-good-deal bounds. We shall provide necessary and sufficient conditions on the fully-dynamic risk measures so that the corresponding risk-indifference prices satisfy the no-good-deal bounds. Remarkably, the use of no-good-deal bounds also provides a method to select the risk measures and thus construct a proper fully-dynamic risk-indifference price system within the $L_2$-spaces.