@article {Ghossoub2015a,
	title = {Vigilant Measures of Risk and the Demand for Contingent Claims},
	journal = {Insurance: Mathematics and Economics},
	volume = {61},
	year = {2015},
	pages = {27-35},
	abstract = {<p>We examine a class of utility maximization problems with a non-necessarily law-invariant utility, and with a non-necessarily law-invariant risk measure constraint. Under a consistency requirement on the risk measure that we call\&nbsp;<em>Vigilance</em>, we show the existence of optimal contingent claims, and we show that such optimal contingent claims exhibit a desired monotonicity property. Vigilance is satisfied by a large class of risk measures, including all distortion risk measures and some classes of robust risk measures. As an illustration, we consider a problem of optimal insurance design where the premium principle satisfies the vigilance property, hence covering a large collection of commonly used premium principles, including premium principles that are not law-invariant. We show the existence of optimal indemnity schedules, and we show that optimal indemnity schedules are nondecreasing functions of the insurable loss.</p>},
	url = {http://www.sciencedirect.com/science/article/pii/S0167668714001619},
	author = {M Ghossoub}
}