A Decision Theoretic Approach to Bid-Ask Spreads.

Preorder representation results are applied to a normative valuation theory for dealers setting bid-ask spreads in a dynamic framework. The preorders induced by ask and bid prices of marketed assets should satisfy some axioms in order for prices not to yield arbitrage opportunities to traders and not to be such that assets could have zero demands. In a discrete time dynamic model for marketed assets with comonotone payoffs (e.g. markets for options on an underlying security or bond markets) the price functional at each date is shown to be a Choquet integral of discounted asset payoffs next period. Such Bid-ask spreads amount for inventory risk.