Seminar announcement: Macci on Large deviations for risk measures models – September 6, 2019 - 15.30-16.30  

Dear Colleagues,

On September 6, 2019, 15.30-16.30, Prof. Claudio Macci (University of Roma Tor Vergata) will give a talk on “Large deviations for risk measures in finite mixture models” (joint with Valeria Bignozzi and Lea Petrella).

Insubria University

Dept. Economics, 

Via Monte Generoso 71

Sala del Consiglio

primo piano

Below you find an abstract of Claudio’s paper. You are all invited.

Best regards,

Elisa Mastrogiacomo

Abstract

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is important to investigate the committed error. In this paper we study the asymptotic behaviour of
estimated risk measures, as the data sample size tends to infinity, in the fashion of large deviations. We obtain large deviation results by applying the contraction principle, and the rate functions are given by a suitable variational formula; explicit expressions are available for mixtures of two models. Finally, our results are applied to the most common risk measures, namely the quantiles, the expected shortfall and the shortfall risk measure.