11 Maggio, 2017 11:15

Sezione di Probabilità e Statistica Matematica

Information uncertainty related to marked random times and optimal investment

Prof. Idris Kharroubi,  Università Paris Dauphine

Sala Maestrale, Tender , piano -1

abstract

abstract

We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider's information flow by using the theory of enlargement of filtrations and then obtain explicit logarithmic utility maximization results to compare optimal wealth for the insider and the ordinary agent. This talk is based on a joint work with Ying Jiao (Université Lyon I).

10 Maggio, 2017 12:15

Seminari di Cultura Matematica

Laser superintensi, materiali nanostrutturati, accelerazione di particelle: il ruolo della matematica

Matteo Passoni, Politecnico di Milano

Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21

We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider's information flow by using the theory of enlargement of filtrations and then obtain explicit logarithmic utility maximization results to compare optimal wealth for the insider and the ordinary agent. This talk is based on a joint work with Ying Jiao (Université Lyon I).

10 Maggio, 2017 14:30

Seminario Matematico e Fisico di Milano

Random walks on dynamic random graphs

Frank den Hollander, Leiden University, The Netherlands

Aula U5-3014 del Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca

abstract

abstract

The mixing time of a random walk is the time it needs to approach its stationary distribution. For random walks on graphs, the characterisation of the mixing time has been the subject of intensive study. One of the motivations is the fact that the mixing time gives information about the geometry of the graph. In the last few years, much attention has been devoted to the analysis of mixing times for random walks on \emph{random graphs}, which poses interesting challenges.

Many real-world networks are dynamic in nature. It is therefore natural to study random walks on \emph{dynamic random graphs}. In this talk we consider a random walk on the configuration model, i.e., a random graph with prescribed degrees. We investigate what happens when at each unit of time a fraction $\alpha_n$ of the edges is randomly relocated, where $n$ is the number of nodes.
We identify \emph{three regimes} for the mixing time in the limit as $n \to \infty$, depending on the choice of $\alpha_n$. These regimes exhibit surprising behaviour.

Joint work with Luca Avena (Leiden), Hakan Guldas (Leiden) and Remco van der Hofstad (Eindhoven)

10 Maggio, 2017 14:15

MOX Seminar

Multi-agent systems. Accuracy guarantees for a class of randomized averaging algorithms

Julien M. Hendrickx, ICTEAM Institute, Université catholique de Louvain, Belgium

Multi-agent systems. Accuracy guarantees for a class of randomized averaging algorithms

abstract

abstract

We consider a class of algorithms meant for averaging data in a decentralized way, but where the value computed might differ from the real average due to asymmetric or asynchronous communications and lost messages. We provide a new general upper bound on the mean difference between the value computed and the initial average.
We particularize our results to various algorithms in the literature (and their generalization), obtaining bounds that match or outperform the previously available ones, and establishing the accuracy of several methods for which the question was open.
We also compare the robustness of these algorithms with that of the push-sum method, which is specifically tailored for directed asynchronous communications.
Our results are based on a novel approach apparently unrelated to the convergence properties of the systems, and lead to bounds depending on local parameters easily controlled by the designer.
Contatto: domenico.brunetto@polimi.it

5 Maggio, 2017 10:30 in punto

Sezione di Probabilità e Statistica Matematica

Invariance under quasi-isometries of subcritical and supercritical behavior in the Boolean model of percolation

Cristian Coletti, Universidade Federal do ABC, Santo André - Sao Paulo, Brasil

Aula seminari del III piano del Dipartimento di Matematica del Politecnico di Milano

abstract

abstract

We study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. More precisely, we prove that if a metric space M is mm-quasi-isometric to another metric space N, and the Poisson Boolean model in M exhibits any of the following: (a) a subcritical phase; (b) a supercritical phase; or (c) a phase transition, then the same does the Poisson Boolean model of percolation in N. We use these results in order to understand the phase transition phenomenon in a large family of metric spaces.

2 Maggio, 2017 14:00 in punto

Sezione di Finanza Quantitativa

Who bears interest rate risk?

Federico Pierobon, Banca Centrale Europe

Aula Seminari Terzo Piano

We study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. More precisely, we prove that if a metric space M is mm-quasi-isometric to another metric space N, and the Poisson Boolean model in M exhibits any of the following: (a) a subcritical phase; (b) a supercritical phase; or (c) a phase transition, then the same does the Poisson Boolean model of percolation in N. We use these results in order to understand the phase transition phenomenon in a large family of metric spaces.

28 Aprile, 2017 14:00

Sezione di Geometria, Algebra e loro applicazioni

Reproducing Kernel Hilbert Spaces in the context of Fractional Derivatives

Paula Cerejeiras, Università di Aveiro

Aula Seminari del 3 piano

abstract

abstract

The idea of a fractional calculus - as already suggested by Leibniz - has seen an increasing interest due to the possibilities for a more accurate description of numerous physical problems either because it provides a new degree of freedom which can be used for more complete characterization of an object or as an additional encoding parameter. In this talk we present a general framework for a function theory based on fractional Cauchy-Riemann operators. Using suitable basic monogenic powers and associated Fueter series we study Gleason's problem and reproducing kernel Hilbert spaces, like the Drury-Arveson space and de Branges-Rovnyak space. We present a counterpart of the Beurling-Lax theorem in the fractional Clifford-Arveson space and give a characterization of the Schur-Agler classes. If time allows we will end with a statement on Schur multipliers in this fractional setting.

27 Aprile, 2017 14:00

MOX Seminar

Energy from ocean waves

Giuseppe Passoni, POLITECNICO DI MILANO, Dipartimento di Elettronica Informazione e Bioingegneria

Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14

abstract

abstract

Electricity generation from clean, safe and sustainable energy sources is one of the main challenges of the 21th century. Ocean waves represent a vast untapped energy source, which could contribute to energy portfolio diversification and to economic growth in coastal regions. Compared to other renewable energy sources, like solar and wind energy, ocean wave power is characterized by higher energy density, less hour-to-hour variability, higher predictability and lower visual impact. Thanks to its huge potential, ocean energy technologies are currently drawing large interest, particularly in the European Union, which is at the forefront in this technological challenge. The European Commission is now implementing a policy framework to support ocean energy with the aim of installing 100 GW of wave and tidal energy capacity by 2050. Although wave energy technologies are still not economically competitive, a number of devices are starting to be rolled out for large scale development and several others are close to prototyping stage. In this context, the mild Mediterranean wave climate, compared to severe ocean climates, has hampered the research until the last few years. However, the interest in wave electricity production is now steadily increasing, particularly in Italy, as highly energetic Atlantic sites have been proven to be too extreme for devices survivability. In this talk, an overview of wave energy production will be given: from the physical concepts, to the assessment of the available resource, to the classification of the different types of wave energy converters (WECs). Then, recent research on wave energy exploitation in Italian seas will be presented. Starting from the feasibility of wave electricity production off the Italian coasts, some existing devices will be analyzed in terms of their performance at some of the most promising Italian locations. After proper rescaling to the Mediterranean wave climate, some of the existing technologies will result into attractive performance parameters, very close to those of more energetic wave climates. The importance of mathematical modeling in wave energy conversion will be illustrated taking the example of a promising point absorber, directly driven by a linear generator and specifically designed for mild wave climates. A key feature of the mathematical model is the coupling between hydrodynamic and electromagnetic kernel, which allows for taking into account the effect of hydrodynamic interactions on the power take off system, as a whole. Numerical models are also essential tools for assessing the overall performance of wave energy farms, i.e. when looking at the topology of arrays of devices with respect to their mutual interactions and power quality issues.

contact: edie.miglio@polimi.it

26 Aprile, 2017 12:30 in punto

Sezione di Finanza Quantitativa

Pricing and Hedging GDP-linked Bonds in Incomplete Markets

Andrea Consiglio, Università di Palermo

Aula Seminari Terzo Piano

abstract

abstract

An old idea was revived at the G20 leaders meeting in Chengdu, China, in July 2016: issuing contingent debt for sovereigns. The International Monetary Fund was asked to analyze the "technicalities, opportunities, and challenges of state-contingent debt instruments, including GDP-linked bonds" and report back within a year. GDP-linked bonds make debt payments contingent on a country’s GDP. Linking payments to GDP growth rate (or nominal value) ensures that debt can always be serviced. GDP-linked instruments were first suggested during the debt crisis of the 1980’s in the context of debt restructuring. Concerned about a country’s growth prospects in the aftermath of a crisis, creditors and debtor Governments sought instruments for risk sharing to increase debt resilience to macroeconomic shocks. An obstacle in issuing GDP-linked bonds is the need for appropriate pricing models. Furthermore, investors in these novel instruments will need to hedge their risk exposure. Our research addresses these two obstacles by developing a pricing model that, by its nature, provides also a hedging portfolio.

26 Aprile, 2017 15:00

Sezione di Finanza Quantitativa

Financial Integration Indicators

Stefano Borgioli, ECB

Aula Seminari Sesto Piano

abstract

abstract

The integration of Europe’s financial markets is an issue of high importance for the Eurosystem. The ECB has been publishing a set of financial integration indicators since 2005. These indicators span many important dimensions of financial systems and assess the degree of integration in the main financial segments of the euro area, namely money, bond, equity and banking markets. Two broad categories of indicators are considered: price-based indicators and quantity-based indicators. Price-based indicators measure discrepancies in asset prices based on their geographic origin. Quantity-based indicators are used to investigate the extent to which investors have internationalised their portfolios. They usefully complement price-based indicators, as in financially integrated markets investors will increase their holdings of non-domestic assets to fully reap the benefits of international diversification. The set of financial integration indicators is published semi-annually on the ECB’s web site. A fully-fledged ECB Report is published annually, with the aim of documenting and monitoring the progress of financial integration in the euro area.