@article {7420,
	title = {A Neyman-Pearson Problem with Ambiguity and Nonlinear Pricing},
	journal = {Mathematics and Financial Economics},
	volume = {12},
	year = {2018},
	pages = {365-385},
	abstract = {<p>
	We consider a problem of the Neyman-Pearson type arising in the theory of portfolio\&nbsp;choice in the presence of probability weighting, such as in markets with Choquet\&nbsp;pricing (as in Araujo et al (2011), Cerreia-Vioglio et al (2015), Chateauneuf and Cornet\&nbsp;(2015), or Chateauneuf et al (1996)) and ambiguous beliefs about the payoffs of\&nbsp;contingent claims. Specifically, we consider a problem of optimal choice of a contingent\&nbsp;claim so as to minimize a non-linear pricing functional (or a distortion risk measure),\&nbsp;subject to a minimum expected performance measure (or a minimum expected return\&nbsp;or utility), where expectations with respect to distorted probabilities are taken in the\&nbsp;sense of Choquet. Such contingent claims are called cost-efficient. We give an\&nbsp;analytical characterization of cost-efficient contingent claims under very mild\&nbsp;assumptions on the probability weighting functions, thereby extending some of the\&nbsp;results of Ghossoub (2016), and we provide examples of some special cases of\&nbsp;interest. In particular, we show how a cost-efficient contingent claim exhibits a\&nbsp;desirable monotonicity property: It is anti-comonotonic with the random mark-to-market\&nbsp;value (or return, etc.) of the underlying financial position, and it is hence a hedge\&nbsp;against such variability.
</p>
},
	url = {https://link.springer.com/article/10.1007\%2Fs11579-017-0207-y},
	author = {Ghossoub, M.}
}
