@article {Ghossoub2016MFE, title = {Cost-Efficient Contingent Claims with Market Frictions}, journal = {Mathematics and Financial Economics}, volume = {10}, number = {1}, year = {2016}, pages = {87-111}, abstract = {

In complete frictionless securities markets under uncertainty, it is well-known that in the absence of arbitrage opportunities, there exists a unique linear positive pricing rule, which induces a state-price density (e.g., Harrison and Kreps (1979)). Dybvig (1988) showed that the cheapest way to acquire a certain distribution of a consumption bundle (or security) is when this bundle is anti-comonotonic with the state-price density, i.e., arranged in reverse order of the state-price density. In this paper, we look at extending Dybvig{\textquoteright}s ideas to complete markets with imperfections represented by a nonlinear pricing rule (e.g., due to bid-ask spreads). We consider an investor in a securities market where the pricing rule is {\textquotedblleft}law-invariant{\textquotedblright} with respect to a capacity (e.g., Choquet pricing as in Araujo et al. (2011),\ Chateauneuf et al. (1996),\ Chateauneuf and Cornet (2015),\ Cerreia-Vioglio et al. (2015). The investor holds a security with a random payoff\ X\ and his problem is that of buying the cheapest contingent claim\ Y\ on\ X, subject to some constraints on the performance of the contingent claim and on its level of risk exposure. The cheapest such claim is called\ cost-efficient. If the capacity satisfies standard continuity and a property called\ strong diffuseness\ introduced in Ghossoub (2015), we show the existence and monotonicity of cost-efficient claims, in the sense that a cost-efficient claim is anti-comonotonic with the underlying security{\textquoteright}s payoff\ X. Strong diffuseness is satisfied by a large collection of capacities, including all distortions of diffuse probability measures. As an illustration, we consider the case of a Choquet pricing functional with respect to a capacity and the case of a Choquet pricing functional with respect to a distorted probability measure. Finally, we consider a simple example in which we derive an explicit analytical form for a cost-efficient claim.

}, url = {https://link.springer.com/article/10.1007/s11579-015-0151-7}, author = {M Ghossoub} }