Workshop in honour of Maurizio Pratelli

PROGRAM

• 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

PARTICIPANTS

• Paolo Baldi (Università di Roma Tor Vergata)
• Anna Battauz (Università Bocconi)
• Fabio Bellini (Università di Milano-Bicocca)
• Francesca Biagini (Universität München )
• Sara Biagini (LUISS)
• Giorgia Callegaro (Università di Padova)
• Lucia Caramellino (Università di Roma Tor Vergata)
• Francesco Cordoni
• Vincenzo Costa (Università di Cassino)
• Marzia De Donno (Università di Parma)
• Freddy Delbaen (ETH Zürich)
• Antonio Di Cesare (Bankitalia)
• Cristina Di Girolami (Università di Pescara)
• Salvatore Federico (Università di Siena)
• Franco Flandoli (Scuola Normale Superiore)
• Hans Föllmer (Humboldt Universität)
• Marco Francischello (Imperial College)
• Marco Frittelli (Università di Milano)
• Rita Giuliano (Università di Pisa)
• Fausto Gozzi (LUISS)
• Paolo Guasoni (Dublin City University)
• Giulia Livieri (Scuola Normale Superiore)
• Cecilia Mancini (Università di Firenze)
• Denise Massa (Università di Pisa)
• Sabrina Mulinacci (Università di Bologna)
• Eni Musta (TU Delft)
• Huyen Pham (Université Paris Diderot)
• Roberto Renò (Università di Verona)
• Marco Romito (Università di Pisa)
• Wolfgang Runggaldier (Università di Padova)
• Marco Tolotti (Università di Venezia)
• Giacomo Toscano (Scuola Normale Superiore)
• Dario Trevisan (Università di Pisa)
• Tiziano Vargiolu (Università di Padova)
• Danilo Vassallo (Scuola Normale Superiore)

Venue

Aula Magna

Dipartimento di Matematica

Università di Pisa

Largo Bruno Pontecorvo 5

56127 Pisa

Italia

Supported by Ludwig-Maximilians Universität München and Università di Pisa (Fondi di ateneo)