  We investigate the structure of good deal bounds, which are subintervals of a
no-arbitrage pricing bound, for financial market models with convex constraints
as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a
good deal bound are naturally described by a convex risk measure. We call such
a risk measure a good deal valuation; and study its properties. We also discuss
superhedging cost and Fundamental Theorem of Asset Pricing for convex
constrained markets.
