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Jozsef Gall: On approximations of Value at Risk and Expected Shortfall involving kurtosis

Date of publication: 15. 4. 2019
Seminar for probability, statistics, and financial mathematics
Četrtek, 18. aprila 2019, ob 14:15 v predavalnici 3.06 na FMF, Jadranska 21, Ljubljana.

V četrtek, 18. aprila 2019, ob 14:15 bo v predavalnici 3.06 Fakultete za matematiko in fiziko Univerze v Ljubljani na Jadranski ulici 21 v Ljubljani potekalo predavanje Jozsefa Galla (University of Debrecen) z naslovom On a family of non-linear optimal martingale transport problems.

Povzetek: We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our approximations are motivated by extensions of the so-called Normal Power Approximation, used for approximating the cumulative distribution function of a random variable, incorporating not only the skewness but the kurtosis of the random variable in question as well. We show the performance of our approximations in numerical examples and we also give comparisons with some known ones in the literature.