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Calculation of Bayes premium for conditional elliptical risks
Affiliation:1. School of Mathematics, Statistics and Actuarial Sciences, University of Kent, Canterbury, CT2 7NF, United Kingdom;2. Actuarial Department, Faculty of Business and Economics, University of Lausanne, Extranef, UNIL-Dorigny, 1015 Lausanne, Switzerland;1. Department of Statistical Sciences, University of Padova, Italy;2. Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Italy;3. Department of Methods and Models for Economics, Territory and Finance, Sapienza University of Rome, Italy;1. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia;2. Institute for Research and Applications of Fuzzy Modeling, Division of University Ostrava, National Super computing Center IT4 Innovations, 30. dubna 22, Ostrava 701 03, Czech Republic;3. Department of Mathematics, Islamic Azad University, Maragheh branch, Maragheh, Iran;1. Department of Finance, School of Economics and Finance, Universidad EAFIT, Carrera 49 No 7 Sur-50, Medellin, Colombia;2. School of Management, Universidad de los Andes, Calle 21 No. 1-20, Bogota, Colombia;3. Department of Economics and IME, University of Salamanca, Campus Miguel de Unamuno, 37007 Salamanca, Spain;1. Research group of Mathematical Analysis, University of Almería, 04120 Almería, Spain;2. Department of Mathematical Sciences, Lewis & Clark College, Portland, OR 97219, USA;3. Department of Applied Mathematics, University of Granada, 18071 Granada, Spain;4. Department of Mathematics, University of Almería, 04120 Almería, Spain;1. Department of Economics, Statistics and Finance, University of Calabria, Italy;2. University of Montenegro, Faculty of Philosophy, Nikšić, Montenegro;3. School of Mathematics, University of Manchester, Manchester, UK;1. Department of Industrial & Systems Engineering, Chung Yuan Christian University, Chungli 32023, Taiwan, ROC;2. Department of Marketing and Distribution Management, Chien Hsin University of Science and Technology, Jungli 32097, Taiwan, ROC;3. Department of Industrial Management, Chien Hsin University of Science and Technology, Jungli 32097, Taiwan, ROC
Abstract:In this paper we discuss the calculation of the Bayes premium for conditionally elliptical multivariate risks. In our framework the prior distribution is allowed to be very general requiring only that its probability density function satisfies some smoothness conditions. Based on the previous results of Landsman and Nešlehová (2008) and Hamada and Valdez (2008) we show in this paper that for conditionally multivariate elliptical risks the calculation of the Bayes premium is closely related to the Brown identity and the celebrated Stein’s lemma.
Keywords:
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