On the estimation of the distribution of aggregated heavy tailed risk
Marie Kratz – ESSEC Business School and CREAR

Extreme events in finance

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The presence of heavy tails has been long recognized for financial and insurance data, which makes the Gaussian distribution a poor approximation of the extreme risks distribution. The main objective of this chapter is to tackle this problem by, on one hand, obtaining the most accurate evaluations of the aggregated risks distribution and thus the risk measures used in solvency regulations, and, on the other hand, by providing practical solutions for estimating high quantiles of aggregated risks.

In this chapter, we explore theoretically as well as numerically new approaches to handle this question, based on properties of upper order statistics and on trimmed sums. We show that these approaches compare very favorably to existing methods, for instance with the one based on the Generalized Central Limit Theorem.

Extreme events in finance Extreme events in finance

Marie Kratz, ESSEC Business School CREAR

Marie Kratz

ESSEC Business School and CREAR