  The seller's risk-indifference price evaluation is studied. We propose a
dynamic risk-indifference pricing criteria derived from a fully-dynamic family
of 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. The family
is then characterised by a double time index. Our framework fits well the study
of both short and long term investments. In this dynamic framework we analyse
whether the risk-indifference pricing criterion actually provides a proper
convex price system, for which time-consistency is guaranteed. It turns out
that the analysis is quite delicate and necessitates an adequate setting. This
entails the use of capacities and an extension of the whole price system to the
Banach spaces derived by the capacity seminorms.
  Furthermore, we consider the relationship of the fully-dynamic
risk-indifference price with no-good-deal bounds. Recall that no-good-deal
pricing guarantees that not only arbitrage opportunities are excluded, but also
all deals that are "too good to be true". 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. The use
of no-good-deal bounds also provides a method to select the risk measures and
then construct a proper fully-dynamic risk-indifference price system in the
$L_2$-spaces.
