Submodular financial markets with frictions

Abstract This paper studies arbitrage-free financial markets with bid-ask spreads whose super-hedging prices are submodular. The submodular assumption on the price, or supermodularity usually assumed utility functions, is formal expression of perfect complementarity, which dates back to Fisher, Pareto, and Edgeworth, according Samuelson (J Econ Lit 12:1255–1289, 1974). Our main contribution provides several characterizations frictions that as a consequence more general study pricing rules. First, market if only its price Choquet integral set risk-neutral probabilities representable core non-additive probability uniquely defined, called capacity. Second, by risk neutral capacity it equivalent market, composed event securities.