- 9:00 Welcome
- 9:20 Hans Föllmer (Humboldt Universität):
Couplings on Wiener space
We discuss couplings on Wiener space, both in terms of measures
on path space and in terms of the corresponding random fields in the
Lévy-Ciesielski representation. In particular we take a fresh
look at the connection between the Wasserstein metric and the relative
entropy with respect to Wiener measure provided by the Talagrand-Feyel-Ustunel
inequality.
Using results of Nina Gantert for large deviations in the quadratic
variation of Brownian motion, we extend this inequality beyond the
absolutely continuous case, using the notion of specific relative entropy.
- 10:00 Marco Frittelli (Università di Milano):
On Fairness of Systemic Risk Measures
In a previous paper, we have introduced a general class of systemic risk measures
that allow random allocations to individual banks before aggregation of their risks.
In the present paper, we address the question of fairness of these allocations and
we propose a fair allocation of the total risk to individual banks.
We show that the dual problem of the minimization problem which identify the systemic
risk measure,
provides a valuation of the random allocations which is fair both from the point of
view of the society/regulator and from the individual financial institutions.
The case with exponential utilities which allows for explicit computation is treated in
details.
- 10:40 Coffee break
- 11:00 Paolo Baldi (Università di Roma Tor Vergata):
Large Deviations et caetera
I shall speak about Large Deviations and how I have seen them in time.
- 11:40 Huyen Pham (Université Paris Diderot):
Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach
This talk is concerned with multi-asset mean-variance portfolio selection problem
under model uncertainty. We develop a continuous time framework for taking into account
ambiguity aversion about both expected rate of return and correlation matrix of stocks,
and for studying the effects on portfolio diversification.
We prove a separation principle for the associated robust control problem, which
allows to reduce the determination of the optimal dynamic strategy to the parametric
computation of the minimal risk premium function. Our results provide a justification
for under-diversification, as documented in empirical studies, and that we explicitly
quantify in terms of correlation and Sharpe ratio ambiguity parameters.
In particular, we show that an investor with a poor confidence in the expected return
estimation does not hold any risky asset, and on the other hand, trades only one risky
asset when the level of ambiguity on correlation matrix is large. This extends to the
continuous-time setting the results obtained by Garlappi, Uppal and Wang (2007), and
Liu and Zeng (2017) in a one-period model.
- 12:20 Wolfgang Runggalddier (Università di Padova):
On approximation methods for mixed singular/non singular stochastic filtering problems
My first scientific contacts with Maurizio concerned approximation
methods for stochastic filtering. This scientific area has experienced various
ups and downs, but it has useful applications in various fields, among them also
financial mathematics. There has been some recent renewed interest also in
singular filtering problems, where the observations are non corrupted by
additive noise. The aim of the talk is to show how approximation methods can be
fruitfully applied to solve filtering problems with mixed singular/non singular
observations.
- 13:00 Lunch break
- 14:00 Paolo Guasoni (Dublin City University):
Asset Prices in Segmented and Integrated Markets
This paper evaluates the effect of market integration on prices and welfare, in
a model where two Lucas trees grow in separate regions with similar investors.
We find equilibrium asset price dynamics and welfare both in segmentation, when
each region holds its own asset and consumes its dividend, and in integration,
when both regions trade both assets and consume both dividends. Integration
always increases welfare. Asset prices may increase or decrease, depending on
the time of integration, but decrease on average. Correlation in assets' returns
is zero or negative before integration, but significantly positive afterwards,
explaining some effects commonly associated with financialization.
- 14:40 Freddy Delbaen (ETH Zürich):
Mod-gaussian convergence for sums of trigonometric functions and similar problems
Salem and Zygmund showed that trigonometric functions with exponents along a lacunary (Hadamard) sequence almost
behave like independent random variables. They satisfy a central limit theorem. We will show that these sequences
even satisfy a better form of convergence, called mod-gaussian. This allows to prove local convergence theorems.
It is easy to see that the theorems do not extend to Sidon sets. Kac showed that for well behaved functions,
doubling the argument gives a sequence that again satisfies a central limit theorem. The work of Kac can be put
in a martingale framework and can be generalised. This is joint work with Emma Hovhannisyan from the Uni-Zurich.
- 15:20 Conclusions and coffee
