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Tail asymptotics of random sum and maximum of log-normal risks
Institution:1. University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland;2. Université de Lyon, F-69622 Lyon, France;3. Université Lyon 1, Laboratoire SAF, EA 2429, Institut de Science Financière et d’Assurances, 50 Avenue Tony Garnier, F-69007 Lyon, France;1. Division of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003, USA;2. Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA;1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark;2. Institut Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg cedex, France;3. Department of Mathematical Statistics and Actuarial Science, University of the Free State, 205 Nelson Mandela drive, Park West, 9300 Bloemfontein, South Africa;1. Department of Mathematics, Tsinghua University, China;2. Institute of Applied Mathematics, AMSS, CAS, Beijing, China;1. Korea University, Seoul, Republic of Korea;2. Seoul National University, Seoul, Republic of Korea;3. Yonsei University, Seoul, Republic of Korea;4. Sookmyung Women’s University, Seoul, Republic of Korea;1. Mathematics Research Unit, University of Luxembourg, Campus Kirchberg, 6 rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Grand-Duchy of Luxembourg, Luxembourg;2. Faculté des Sciences de Tunis, Campus Universitaire 2092 - El Manar Tunis, Tunisie
Abstract:In this paper we derive the asymptotic behaviour of the survival function of both random sum and random maximum of log-normal risks. As for the case of finite sum and maximum investigated in Asmussen and Rojas-Nandayapa (2008) also for the more general setup of random sums and random maximum the principle of a single big jump holds. We investigate both the log-normal sequences and some related dependence structures motivated by stationary Gaussian sequences.
Keywords:Risk aggregation  Log-normal risks  Exact asymptotics  Gaussian distribution  Product of random variables
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