@article{55ad4111f88d4c53891f3035026311ca,
title = "Conditional Davis pricing",
abstract = "We study the set of Davis (marginal utility-based) prices of a financial derivative in the case where the investor has a non-replicable random endowment. We give a new characterisation of the set of all such prices, and provide an example showing that even in the simplest of settings – such as Samuelson{\textquoteright}s geometric Brownian motion model –, the interval of Davis prices is often a non-degenerate subinterval of the set of all no-arbitrage prices. This is in stark contrast to the case with a constant or replicable endowment where non-uniqueness of Davis prices is exceptional. We provide formulas for the endpoints of these intervals and illustrate the theory with several examples.",
keywords = "Incomplete markets, Marginal utility-based pricing, Non-smoothness, Unspanned endowment, Utility maximisation",
author = "Kasper Larsen and Soner, {Halil Mete} and Gordan {\v Z}itkovi{\'c}",
note = "Funding Information: The authors would like to thank Martin Schweizer, Pietro Siorpaes, Mihai S{\^i}rbu, Kim Weston, our Co-Editor Alex Schied, and our anonymous AE and reviewers for numerous and helpful suggestions. During the preparation of this work, the first author has been supported by the National Science Foundation under Grant No. DMS-1411809 (2014–2017) and Grant No. DMS-1812679 (2018–2021), the second author has been supported by the Swiss National Foundation through the grant SNF and by the Swiss Finance Institute, and the third author has been supported by the National Science Foundation under Grant No. DMS-1107465 (2012–2017), Grant No. DMS-1516165 (2015–2018), and Grant No. DMS-1815017 (2018–2021). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF). Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2020",
month = jul,
day = "1",
doi = "10.1007/s00780-020-00424-5",
language = "English (US)",
volume = "24",
pages = "565--599",
journal = "Finance and Stochastics",
issn = "0949-2984",
publisher = "Springer Verlag",
number = "3",
}