Risk concentration based on Expectiles for extreme risks under FGM copula |
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| Affiliation: | 1. Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, China;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada;1. Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada;3. Actuarial Science Program, Drake University, Des Moines, IA 50311, USA;1. Department of Financial Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, China;2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China;3. LMEQF, Department of Financial Mathematics and Center for Statistical Sciences, Peking University, Beijing, 100871, China;1. Department of Applied Finance & Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney NSW 2109, Australia;2. School of Mathematical Sciences, Faculty of Science and Technology, National University of Malaysia, 43600 Bangi, Selangor, Malaysia |
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| Abstract: | Risk concentration is used as a measurement of diversification benefits in the context of risk aggregation. Expectiles, which are known to possess many good properties, have attracted increasing interest in recent years. In this paper, we aim to study the asymptotic properties of risk concentration based on Expectiles. Firstly, we extend the results on the second-order asymptotics of Expectiles in Mao et al. (2015). Secondly, we investigate the second-order asymptotics of tail probabilities and then apply them to risk concentrations based on Expectiles as well as on VaR. |
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| Keywords: | Expectiles FGM copula Regular variation Second-order regular variation Value-at-Risk |
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