@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 = {<p>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),\&nbsp;Chateauneuf et al. (1996),\&nbsp;Chateauneuf and Cornet (2015),\&nbsp;Cerreia-Vioglio et al. (2015). The investor holds a security with a random payoff\&nbsp;<em>X</em>\&nbsp;and his problem is that of buying the cheapest contingent claim\&nbsp;<em>Y</em>\&nbsp;on\&nbsp;<em>X</em>, subject to some constraints on the performance of the contingent claim and on its level of risk exposure. The cheapest such claim is called\&nbsp;<em>cost-efficient</em>. If the capacity satisfies standard continuity and a property called\&nbsp;<em>strong diffuseness</em>\&nbsp;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\&nbsp;<em>X</em>. 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.</p>},
	url = {https://link.springer.com/article/10.1007/s11579-015-0151-7},
	author = {M Ghossoub}
}