Fourier-analytic measures for heavy-tailed insurance losses |
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| Authors: | Michael R. Powers Thomas Y. Powers |
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| Affiliation: | 1. School of Economics and Management, Tsinghua University, Beijing, China.powers@sem.tsinghua.edu.cn;3. Business Economics, Harvard Business School, Cambridge, MA, USA. |
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| Abstract: | We propose a family of three ‘Fourier-analytic’ measures to extend the conventional concepts of standard deviation, variance, and coefficient of variation to insurance losses with arbitrarily heavy tails. After motivating and computing their mathematical forms, we apply the proposed measures to the case of Lévy-stable loss portfolios. Finally, the new measures are used to study the diversification properties of heavy-tailed losses. |
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| Keywords: | risk measure deviation measure insurance losses heavy tails Fourier analysis Lévy-stable family additivity diversification |
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