We study convex risk measures describing the upper and lower bounds of a good
deal bound, which is a subinterval of a no-arbitrage pricing bound. We call
such a convex risk measure a good deal valuation and give a set of equivalent
conditions for its existence in terms of market. A good deal valuation is
characterized by several equivalent properties and in particular, we see that a
convex risk measure is a good deal valuation only if it is given as a risk
indifference price. An application to shortfall risk measure is given. In
addition, we show that the no-free-lunch (NFL) condition is equivalent to the
existence of a relevant convex risk measure which is a good deal valuation. The
relevance turns out to be a condition for a good deal valuation to be
reasonable. Further we investigate conditions under which any good deal
valuation is relevant