Conditional Davis Pricing
35 Pages Posted: 9 May 2018 Last revised: 21 Aug 2018
Date Written: February 7, 2017
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.
Keywords: Incomplete markets, utility-maximization, unspanned endowment, local martingales, linearization, directional derivative
JEL Classification: C61, G11
Suggested Citation: Suggested Citation