Updating pricing rules

  • Aloisio Araujo
  • Alain Chateauneuf
  • José Heleno Faro
  • Bruno Holanda
Research Article


This paper studies the problem of updating the super-replication prices of arbitrage-free finite financial markets with a frictionless bond. Any super-replication price is a pricing rule represented as the support function of some polytope of probabilities containing at least one strict positive probability, which captures the closure of the set of risk-neutral probabilities of any underlying market consistent with the given pricing rule. We show that a weak form of dynamic consistency characterizes the full (prior-by-prior) Bayesian updating of pricing rules. In order to study the problem of updating pricing rules revealing incomplete markets without frictions on all tradable securities, we first show that the corresponding polytope of probabilities must be non-expansible. We find that the full Bayesian updating does not preserve non-expansibility, unless a condition of non-trivial updating is satisfied. Finally, we show that the full Bayesian updating of pricing rules of efficient complete markets is completely stable. We also show that efficient complete markets with uniform bid–ask spreads are stable under full Bayesian updating, while efficient complete markets that fulfill the put–call parity are stable only under a Choquet pricing rule computed with respect to a regular concave nonadditive risk-neutral probability.


Pricing rules Full Bayesian update Incomplete markets Efficient complete markets Bid–ask spreads 

JEL Classification

D52 D53 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IMPARio de JaneiroBrazil
  2. 2.Brazilian School of Economics and FinanceFGV EPGERio de JaneiroBrazil
  3. 3.Research Department in EconomicsIPAG Business SchoolParis Cedex 05France
  4. 4.Paris School of EconomicsUniversité de Paris IParis Cedex 13France
  5. 5.InsperVila OlímpiaBrazil
  6. 6.Faculdade de Administraçño, Contabilidade e EconomiaUniversidade Federal de GoiásGoiâniaBrazil

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