Before revision:  Our ultimate goal is to use utility theory to price non-replicable contingent claims in the case when the investor 's portfolio already contains a non-replicable component. 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:  Our ultimate goal is to use utility theory to price non-replicable contingent claims in the case when the investor 's portfolio already contains a non-replicable random endowment. We provide an example showing 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.