 Optimal measure preserving derivatives revisitedMathematical Finance, 2023, vol. 33, issue 2, 370-388 Abstract: This article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The relationship depends on whether the payoff distribution of the market portfolio satisfies a technical condition called adequacy, meaning that it is atomless or is comprised of finitely many equally probable atoms. Under adequacy, pricing kernel nonmonotonicity is equivalent to the existence of a strong form of stochastic arbitrage involving distributional replication of the market portfolio at a lower price. If the adequacy condition is dropped then this equivalence no longer holds, but pricing kernel nonmonotonicity remains equivalent to the existence of a weaker form of stochastic arbitrage involving second‐order stochastic dominance of the market portfolio at a lower price. A generalization of the optimal measure preserving derivative is obtained, which achieves distributional replication at the minimum cost of all second‐order stochastically dominant securities under adequacy. Date: 2023 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:33:y:2023:i:2:p:370-388 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematical Finance is currently edited by Jerome Detemple More articles in Mathematical Finance from Wiley Blackwell |
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