The theory of asset pricing has traditionally been developed under the two central assumptions of frictionless markets and the absence of arbitrage opportunities. To capture a broader range of frictions observed in financial markets, pricing rules have been studied within a subadditive framework. A significant advance was achieved by [12, 13], who extended the Fundamental Theorem of Finance by showing that, in the presence of market frictions, the validity of put-call parity is equivalent to the representation of the market pricing rule as a discounted Choquet expectation with respect to a risk-neutral, nonadditive probability measure, which in general need not be submodular (concave). This result established a pricing framework beyond subadditivity. Building on this development, the present paper studies Choquet pricing rules in a setting where neither subadditivity nor monotonicity is imposed. We characterize arbitrage-free market pricing rules through two equivalent conditions: (i) the existence of a linear stochastic discount factor dominated by the pricing rule, and (ii) the nonemptiness of the core of the associated risk-neutral nonadditive probability. As an additional contribution, our framework provides an alternative proof of Schmeidler’s theorem on the nonemptiness of the core in an infinite-dimensional cooperative game theory context.
