On behalf of the Scientific Committee of the "B. de Finetti Risk
Seminars, Milano Lectures on the Mathematical Theory of Economics and
Finance”, we are glad to invite you to participate at the following Lecture:
Felix Liebrich
Hannover University, Germany
Title: A tale of one (or many) probabilities.
Abstract:
A crucial condition that allows to establish that two probability charges
lambda-system agree is Marinacci’s Uniqueness Theorem (MUT). A countably
additive probability charge Q and a convex-ranged probability charge P
agree if there is a nontrivial event such that Q is constant on the
generated P-equilikelihood class. Special cases of the MUT can be derived
from Lyapunov’s Convexity Theorem and the sharp version of the
Fréchet-Hoeffding bounds. A further alternative formulation of the
assumption of the MUT is that the Q-expectation functional on simple random
variables is locally P-invariant. It is this overlap between invariance and
uniqueness that is the focus of the talk.
We look at functionals defined on random variables that are globally
invariant with respect to a reference probability P. Fixing a functional we
ask the uniqueness question: Can there be more than one such such reference
probability? For wide classes of functionals, we see that this is not the
case unless they are (i) constant, or (ii) more generally depend only on
the essential supremum and essential infimum of the argument.
In the second part of the talk we return to the MUT and the recent, but
significant extension provided by Svistula that dispenses with the
countable additivity of Q. We expand and clarify the nature of the
Svistula-MUT and uncover several equivalent conditions that enhance the
applicability of said result. As a consequence, we present several
applications.
LOCATION:
The seminar will be held on *September 28, *2022 at *18.00,*
Conference hall 3-E4-SR03, Dept. of Decision Sciences, Bocconi University,
Via G. Roentgen 1, Milan.
Scientific Committee
Prof. Simone Cerreia-Voglio (Univ. Bocconi)
Prof. Marco Frittelli (Univ. degli Studi di Milano)
Prof. Fabio Maccheroni (Univ. Bocconi)
Prof. Marco Maggis (Univ. degli Studi di Milano)
Prof. Massimo Marinacci (Univ. Bocconi)
Prof. Emanuela Rosazza Gianin (Univ. Milano-Bicocca)
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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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