Il Prof. Claudio MACCI dell'Università di Roma Tor Vergata mercoledì 4 dicembre 2019 alle ore 16 nell'Aula E al III livello del Dipartimento di Matematica e Applicazioni dell'Università degli Studi di Napoli Federico II terrà un seminario dal titolo:

Large deviations for risk measures in finite mixture models

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. Joint work with Valeria Bignozzi and Lea Petrella.

La proponente Maria Longobardi