Preprint A598/2008
Revealing Incomplete Financial Markets

JosÃ© Heleno Faro | Araujo, Aloisio | Chateauneuf, Alain

**Keywords: **
Incomplete markets | incomplete prices | superhedging | risk neutral probabilities

Incomplete financial markets without arbitrage opportunities are characterized by the existence of multiple risk neutral probabilities. In this context, a cost function describes the minimum amount necessary for superhedging strategies and it can be recovered from the worst monetary expectation among the whole set of risk neutral probabilities. This paper characterizes the class of non-linear functions, called incomplete prices, that can be viewed as a cost function of frictionless financial markets without arbitrage opportunities in the two periods framework. First, we obtain some criteria that allow to know if a given function is actually an incomplete price. Interestingly, a new role for prices is given because we can recover the market struture from any incomplete price, clarifying the understanding about the interdependence between the market structure and the functional form of incomplete prices. For instance, a
financial markets with a Riesz subspace of attanaible claims is in fact a 'partition market' of bets and such markets are revealed by an incomplete price given by a Choquet integral with respect to a particular concave capacity.