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,
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Conference hall 3-E4-SR03, Dept. of Decision
Sciences, Bocconi University, Via G. Roentgen 1, Milan.
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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)