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Time-inconsistency of VaR and time-consistent alternatives
Authors:Patrick Cheridito  Mitja Stadje
Institution:1. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of China, Hunan Normal University, Changsha 410081, China;2. Department of Mathematics, Hunan University of Finance and Economics, Changsha 410205, China;1. School of Management, Guangdong University of Technology, Guangzhou 510006, PR China;2. Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, PR China;3. Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, PR China;1. Laboratoire de Probabilités et Modèles aléatoires (LPMA), UPMC-Sorbonne Université, UMR 7599, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France;2. Laboratoire de Mathématiques et Modélisation d’Evry (LaMME), UMR 8071, 23 Boulevard de France, 91037 Évry, & ENSIIE, France
Abstract:We show that VaR (Value-at-Risk) is not time-consistent and discuss examples where this can lead to dynamically inconsistent behavior. Then we propose two time-consistent alternatives to VaR. The first one is a composition of one-period VaR's. It is time-consistent but not coherent. The second one is a composition of average VaR's. It is a time-consistent coherent risk measure.
Keywords:
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