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Second order risk aggregation with the Bernstein copula
Institution:1. Université de Lyon, Université Lyon 1, Institut Camille Jordan ICJ UMR 5208 CNRS, France;2. Université de Lyon, Université Lyon 1, Laboratoire SAF EA2429, France;1. Department of Finance, National Chung Cheng University, Minhsiung, 621, Taiwan;2. Risk and Insurance Research Center, National Chengchi University, Taipei, Taiwan;3. Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada;1. China Financial Policy Research Center, School of Finance, Renmin University of China, No. 59 Zhongguancun Street, Haidian District, Beijing 100872, PR China;2. Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA;3. Department of Risk Management, The Pennsylvania State University, 362 Business Building, University Park, PA 16802, USA;1. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, CH-1015 Lausanne, Switzerland;2. Swiss Finance Institute, Lausanne, Switzerland;3. School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, Sydney, NSW 2052, Australia;4. Department of Statistics and Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA
Abstract:We analyze the tail of the sum of two random variables when the dependence structure is driven by the Bernstein family of copulas. We consider exponential and Pareto distributions as marginals. We show that the first term in the asymptotic behavior of the sum is not driven by the dependence structure when a Pareto random variable is involved. Consequences on the Value-at-Risk are derived and examples are discussed.
Keywords:Risk aggregation  Tail asymptotics  Bernstein copula  Value-at-Risk  Pareto and exponential variables
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