Conditional Davis pricing

Kasper Larsen, Halil Mete Soner, Gordan Žitković

Research output: Contribution to journalArticle

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’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.

Original languageEnglish (US)
Pages (from-to)565-599
Number of pages35
JournalFinance and Stochastics
Volume24
Issue number3
DOIs
StatePublished - Jul 1 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

Keywords

  • Incomplete markets
  • Marginal utility-based pricing
  • Non-smoothness
  • Unspanned endowment
  • Utility maximisation

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