Conditional Davis pricing

Kasper Larsen (), Halil Mete Soner () and Gordan Žitković ()
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Kasper Larsen: Rutgers University
Halil Mete Soner: Princeton University
Gordan Žitković: University of Texas at Austin

Finance and Stochastics, 2020, vol. 24, issue 3, No 1, 565-599

Abstract: 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.

Keywords: Unspanned endowment; Incomplete markets; Utility maximisation; Non-smoothness; Marginal utility-based pricing; 91G10; 91G80; 60K35 (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00780-020-00424-5

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