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Title: On the properties of $\Lambda$-quantiles Authors:  Fabio Bellini - University of Milano-Bicocca (Italy) [presenting]
Ilaria Peri - Birkbeck-University of London (United Kingdom)
Abstract: The aim is to study the properties of a family of risk measures recently introduced in the financial literature under the name of $\Lambda$-Value at Risk, that provides an interesting generalization of the usual quantiles. We provide an axiomatic foundation for $\Lambda$-quantiles, similar in spirit to analogous axiomatizations of the usual quantiles. Under mild technical conditions, we characterize the class of scoring functions that are strictly consistent with the $\Lambda$-quantile interval, generalizing the corresponding class of GPL functions that elicits the usual quantiles. Finally, we discuss financial applications of $\Lambda$-quantiles forecasting by means of regression techniques.