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Conditional Davis pricing

Author

Listed:
  • Kasper Larsen

    (Rutgers University)

  • Halil Mete Soner

    (Princeton University)

  • Gordan Žitković

    (University of Texas at Austin)

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.

Suggested Citation

  • Kasper Larsen & Halil Mete Soner & Gordan Žitković, 2020. "Conditional Davis pricing," Finance and Stochastics, Springer, vol. 24(3), pages 565-599, July.
  • Handle: RePEc:spr:finsto:v:24:y:2020:i:3:d:10.1007_s00780-020-00424-5
    DOI: 10.1007/s00780-020-00424-5
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    References listed on IDEAS

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    More about this item

    Keywords

    Unspanned endowment; Incomplete markets; Utility maximisation; Non-smoothness; Marginal utility-based pricing;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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