A nonsmooth approach to nonexpected utility theory under risk |
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| Institution: | 1. Pennsylvania State University, United States;2. University of North Carolina, Chapel Hill, United States;1. Institute of Clinical Pharmacology, Goethe – University, Theodor Stern Kai 7, 60590 Frankfurt am Main, Germany;2. Fraunhofer Institute of Molecular Biology and Applied Ecology – Project Group Translational Medicine and Pharmacology (IME-TMP), Theodor – Stern – Kai 7, 60590 Frankfurt am Main, Germany;3. Smell & Taste Clinic, Department of Otorhinolaryngology, TU Dresden, Fetscherstrasse 74, 01307 Dresden, Germany;1. Department of Business Education, National Changhua University of Education, Changhua 50058, Taiwan;2. Social and Data Science Research Center, Hwa-Kang Xing-Ye Foundation, Taipei 10659, Taiwan;3. Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan;1. State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China;2. Department of Mathematics, Columbia House, London School of Economics, Houghton St., London, WC2A 2AE, United Kingdom;1. Department of Economics, Virginia Polytechnic Institute & State University (Virginia Tech), Blacksburg, VA 24061-0316, USA;2. Université Paris-Dauphine, LEDa Place du Maréchal de Lattre de Tassigny, 75 775 Paris cedex 16, France;1. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia;2. UTIA CAS, Pod Vodárenskou věží 4, 182 08 Prague, Czech Republic;3. School of Sciences, Communication University of China, Beijing 100024, China;4. Singidunum University, 11000 Belgrade, Serbia;5. Óbuda University, H-1034 Budapest, Hungary |
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| Abstract: | We consider concave and Lipschitz continuous preference functionals over monetary lotteries. We show that they possess an envelope representation, as the minimum of a bounded family of continuous vN-M preference functionals. This allows us to use an envelope theorem to show that results from local utility analysis still hold in our setting, without any further differentiability assumptions on the preference functionals. Finally, we provide an axiomatisation of a class of concave preference functionals that are Lipschitz. |
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