# Conditional Davis Pricing

## TL;DR

This paper investigates the set of marginal utility-based prices for financial derivatives with non-replicable endowments, revealing that these prices can form a strict subset of no-arbitrage prices even in simple models.

## Contribution

It introduces formulas for the endpoints of the marginal utility-based price interval and highlights the non-uniqueness phenomenon in non-replicable endowment settings.

## Key findings

- The price interval can be a strict subset of no-arbitrage prices.
- Non-uniqueness of prices is common with non-replicable endowments.
- Formulas for the endpoints of the price interval are provided.

## Abstract

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.