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