Fundamental theorems of asset pricing for good deal bounds

Jeremy Staum*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

We prove fundamental theorems of asset pricing for good deal bounds in incomplete markets. These theorems relate arbitrage-freedom and uniqueness of prices for over-the-counter derivatives to existence and uniqueness of a pricing kernel that is consistent with market prices and the acceptance set of good deals. They are proved using duality of convex optimization in locally convex linear topological spaces. The concepts investigated are closely related to convex and coherent risk measures, exact functionals, and coherent lower previsions in the theory of imprecise probabilities.

Original languageEnglish (US)
Pages (from-to)141-161
Number of pages21
JournalMathematical Finance
Volume14
Issue number2
DOIs
StatePublished - Apr 2004

Keywords

  • Asset pricing
  • Coherent risk measure
  • Convex risk measure
  • Equivalent martingale measure
  • Fundamental theorem
  • Good deal bounds
  • Imprecise probabilities
  • Incomplete markets

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

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