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Second Order Asymptotics of Aggregated Log-Elliptical Risk
Authors:Dominik Kortschak  Enkelejd Hashorva
Institution:1. Université de Lyon, 69622, Lyon, France
2. Laboratoire SAF, EA 2429, Institut de Science Financière et d’Assurances, Université Lyon 1, 50 Avenue Tony Garnier, 69007, Lyon, France
3. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015, Lausanne, Switzerland
Abstract:In this paper we establish the error rate of first order asymptotic approximation for the tail probability of sums of log-elliptical risks. Our approach is motivated by extreme value theory which allows us to impose only some weak asymptotic conditions satisfied in particular by log-normal risks. Given the wide range of applications of the log-normal model in finance and insurance our result is of interest for both rare-event simulations and numerical calculations. We present numerical examples which illustrate that the second order approximation derived in this paper significantly improves over the first order approximation.
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