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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D. Kortschak was supported by the the MIRACCLE-GICC project and the Chaire d’excellence “Generali—Actuariat responsable: gestion des risques naturels et changements climatiques.” E. Hashorva kindly acknowledges partial support by Swiss National Science Foundation Grants 200021-134785 and 200021-1401633/1 and by RARE -318984, a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme.
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Kortschak, D., Hashorva, E. Second Order Asymptotics of Aggregated Log-Elliptical Risk. Methodol Comput Appl Probab 16, 969–985 (2014). https://doi.org/10.1007/s11009-013-9356-5
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DOI: https://doi.org/10.1007/s11009-013-9356-5
Keywords
- Risk aggregation
- Second order asymptotics
- Log-elliptical distribution
- Log-normal distribution
- Gumbel max-domain of attraction