Characterizing Arbitrage-Free Choquet Pricing Rules

The fundamental theory of asset pricing has been developed under the two main assumptions that markets are frictionless and have no arbitrage opportunities. In order to take into account general types of frictions in financial markets, market pricing rules have been studied in the subadditive framework. Recently, Cerreia-Vioglio et al. (2015a,b) have extended the Fundamental Theorem of Finance by showing that, with market frictions, requiring the put-call parity to hold is equivalent to the market pricing rule being represented as a discounted Choquet nonadditive expectation with respect to a risk-neutral nonadditive probability, providing a framework in which pricing is not subadditive. This paper continues the study of Choquet pricing rules that are neither assumed to be subadditive nor monotone and provides characterizations of arbitrage-free market pricing rules, in terms of the existence of a linear stochastic discount factor below the pricing rule, or in terms of the nonvacuity of the core of the risk-neutral nonadditive probability associated with the pricing rule. Interestingly though, this approach allows us to provide an alternative proof to Schmeidler's theorem on the nonvacuity of the core in an infinite dimensional model of cooperative game theory.