We introduce the notion of a conditional Davis price and study its properties. 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. Our main result characterizes this set and provides simple conditions under which its two endpoints can be effectively computed. We illustrate the theory with several examples.
We study the set of marginal utility-based prices of a financial derivative in the case where the investor has a non-replicable random endowment. We provide an example showing that even in the simplest of settings - such as Samuelson's geometric Brownian motion model - the interval of marginal utility-based prices can be a non-trivial strict subinterval of the set of all no-arbitrage prices. This is in stark contrast to the case with a replicable endowment where non- uniqueness is exceptional. We provide formulas for the end points for these prices and illustrate the theory with several examples.
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introduce the notion of a conditional Davis price and study its properties. Our ultimate goal is to use utility theory to price non-replicable contingent claims
study the set of marginal utility-based prices of a financial derivative
R
when the investor 's portfolio already contains
where the investor has
R
component. We show
random endowment. We provide an example showing
A
geometric Brownian motion
R
conditional Davis prices are typically not unique and form
the interval of marginal utility-based prices can be
A
strict
R
Our main result characterizes this set and provides simple conditions under which its two endpoints can be effectively computed. We
This is in stark contrast to the case with a replicable endowment where non- uniqueness is exceptional. We provide formulas for the end points for these prices and