Before revision:  We show that even in the simplest of settings - such as Samuelson's  model - conditional Davis prices are typically not unique and form a non-trivial  subinterval of the set of all no-arbitrage prices.
After revision:  We show that even in the simplest of settings - such as Samuelson's geometric Brownian motion model - conditional Davis prices are typically not unique and form a non-trivial subinterval of the set of all no-arbitrage prices.