Dear all,
you are all invited to participate to the following seminar on *Tuesday
10th of September 2024 at 16:30* in Aula Seminari Demografica 2062 at
University of Milano Bicocca (via degli Arcimboldi 8, Milano - building U7,
2nd floor):
*Speaker: *Felix-Benedikt Liebrich (Univ. of Amsterdam)
*Title:* The (?) reference measure
*Abstract:* A functional on random variables is law invariant with respect
to a reference probability (or probabilistically sophisticated) if its
value only depends on the distribution of its argument under that measure.
The class of such functionals is not only vast, but of integral importance
for financial, actuarial, and economic applications.
In this talk, we take a concrete functional as given and ask (i) if there
can be more than one such reference probability, and (ii) how one can infer
the reference probability from the functional. This stance is in contrast
to wide parts of the literature that treat the reference probability as
given.
Nevertheless, as I will show at the beginning of my talk, it is in line
with the investigation of probabilistically sophisticated preferences and
arises as a natural consequence of the Marinacci-Svistula Uniqueness
Theorem.
Concerning question (i), I demonstrate that uniqueness holds for a wide
class of functionals unless they are constant or depend only on the
essential supremum and essential infimum of the argument. Applications to
monetary and return risk measures will be given.
Concerning the calibration question (ii), I show how to infer the reference
measure as a related supremum or infimum in the space of bounded charges.
While this approach is generally versatile, it fails in the important case
of the Value-at-Risk. Here, a suitable alternative is presented.
Best wishes,
Emanuela
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Emanuela Rosazza Gianin
Dipartimento di Statistica e Metodi Quantitativi
Università di Milano-Bicocca
Edificio U7 – 4° Piano
Via Bicocca degli Arcimboldi, 8
20126 Milano
Tel. 02 64483208
e-mail: emanuela.rosazza1(a)unimib.it
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