<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M Ghossoub</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Vigilant Measures of Risk and the Demand for Contingent Claims</style></title><secondary-title><style face="normal" font="default" size="100%">Insurance: Mathematics and Economics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/pii/S0167668714001619</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">61</style></volume><pages><style face="normal" font="default" size="100%">27-35</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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&amp;nbsp;&lt;em&gt;Vigilance&lt;/em&gt;, 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.&lt;/p&gt;</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record></records></xml>