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.