Past talks

Second semester 2022/2023

• • Fri 10 March, 2023.  Aula 4, Palazzo Campana, 15:00-16:00
    Roxana Dumitrescu (King's College London)
    Title: Optimal stopping mean-field games: a linear programming formulation and applications to entry-exit games in electricity markets
    Abstract:  In this talk, we present recent results on the linear programming approach to stopping mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider mean-field game problems where the representative agent chooses the optimal time to exit the game, where the instantaneous reward function and the coefficients of the state process may depend on the distribution of the other agents. Furthermore, we establish the equivalence between mean-field games equilibria obtained by the linear programming approach and the ones obtained via other approaches used in the previous literature. We then present a fictious play algorithm to approximate the mean-field game population dynamics in the context of the linear programming approach. Finally, we give an application of the theoretical and numerical contributions introduced in the first part of the talk to an entry-exit game in electricity markets. The talk is based on several works, joint with R. Aïd, G. Bouveret, M. Leutscher and P. Tankov.
    
    

  • Wed 15 March, 2023.  Aula 4, Palazzo Campana, 15:00-16:00
    Stefano Pagliarani (University of Bologna)
    Title: Optimal Schauder estimates for degenerate Kolmogorov equations with rough coefficients
    Abstract:  We prove Schauder estimates for a class of degenerate equations satisfying a parabolic Hörmander-type condition, with coefficients that are measurable in time and Hölder continuous in the space variables. We prove our estimates in  Hölder spaces defined in terms of the intrinsic geometry induced by the differential operator, which are the strongest possible under the aforementioned assumptions on the coefficients. Our estimates are global in that they hold up to the boundary, with an explosion factor that depends on the regularity of the boundary condition. The technique we employ relies on the regularity properties of the fundamental solution, which is constructed by means of the so-called parametrix method. These results are key to study the backward Kolmogorov equations associated to a class of degenerate Langevin-type diffusions, with the kinetic setting being a particular case.
    
    

  • Wed 29 March, 2023.  Aula 4, Palazzo Campana, 15:00-16:00
    Pierre Patie (Cornell University)
    Title:  Is self-similarity unique?
    Abstract: Self-similarity is a fundamental and useful property in the study of stochastic processes. In this talk, we will revisit  the classical notion of self-similarity resorting to group representation theory. We shall explain how this viewpoint enables to define self-similarity in a broader context. We will provide examples illustrating this idea and describe some interesting stochastic and analytical implications of this approach.
    
    

  • Wed 5 April, 2023.  Aula 4, Palazzo Campana, 15:00-16:00
    Giacomo Ascione (Scuola Superiore Meridionale)
    Title: The mean length inequality: a quantitative estimate via mass transportation
    Abstract: Let K ⊆ R^d be a compact set and PK, QK ∈ K be two independently selected points, according to the uniform distribution on K. In [2, 3] the authors proved that, for any non-increasing function f, the following inequality holds

(1) E[f(|PK − QK|)] ≤ E[f(|PB − QB|)],

where B is a ball with the same volume of K, and equality holds if and only if K is a ball. The converse inequality, occurring if f is non-decreasing and extended to all intrinsic volumes, has been proven in [7, 8]. Such an inequality can be seen as a direct consequence of Riesz rearrangement inequality and provides one of the simplest examples of randomized isoperimetric inequality. The recent developments of the theory of quantitative isoperimetric inequalities [5] suggests the possibility of using the isoperimetric deficit | E[f(|PK − QK|)] − E[f(|PB − QB|)]| to control, in some sense, the discrepancy between the compact set K and a ball B with the same volume. This has been done, in case f(r) = r^α for some α > −d, independently and with different strategies, in [4] and [6, 1]. In this talk, we will focus on the mass transportation strategy provided first in [6] in the case α < 0 and then extended in [1] for α > 0, underlining the non-trivial differences between the two cases. Finally, if time permits it, we will present an application to a Gamow-like liquid drop model, in which the energy exhibits both repulsive and attractive terms, together with a surface area penalization.

References:
[1] G. Ascione. A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem. ESAIM: Control, Optimisation and Calculus of Variations, 28:4, 2022.
[2] W. Blaschke. Eine isoperimetrische Eigenschaft des Kreises. Mathematische Zeitschrift, 1:52–57, 1918.
[3] T. Carleman. Uber eine isoperimetrische Aufgabe und ihre physikalischen Anwendungen. Mathematische Zeitschrift, 3(1):1–7, 1919.
[4] R. L. Frank and E. H. Lieb. Proof of spherical flocking based on quantitative rearrangement inequalities. Annali della Scuola Normale Superiore, Classe i Scienze, pages 1241–1263, 2021.
[5] N. Fusco. The quantitative isoperimetric inequality and related topics. Bulletin of Mathematical Sciences, 5:517–607, 2015.
[6] N. Fusco and A. Pratelli. Sharp stability for the Riesz potential. ESAIM: Control, Optimisation and Calculus of Variations, 26:113, 2020.
[7] H. Groemer. On some mean values associated with a randomly selected simplex in a convex set. Pacific Journal of Mathematics, 45(2):525–533, 1973.
[8] R. E. Pfiefer. Maximum and minimum sets for for some geometric mean values. Journal of Theoretical Probability, 3:169–179, 1990.

• • Wed 19 April, 2023. Aula 4, Palazzo Campana, 15:00-16:00
    Stephane Menozzi (University of Evry)
    Title:  Convergence Rate of the Euler-Maruyama Scheme Applied to Diffusion Processes with Lq−Lp Drift Coefficient and Additive Noise
    Abstract:  We are interested in the time discretization of stochastic differential equations with additive d-dimensional Brownian noise and L q − L ρ drift coefficient when the condition d/p + 2/q < 1, under which Krylov and Röckner (PTRF, 05) proved existence of a unique strong solution, is met. We show weak convergence with order 1/2 (1 − (d/p + 2/q)) which corresponds to half the distance to the threshold for the Euler scheme with randomized time variable and cutoffed drift coefficient so that its contribution on each time-step does not dominate the Brownian contribution. More precisely, we prove that both the diffusion and this Euler scheme admit transition densities and that the difference between these densities is bounded from above by the time-step to this order multiplied by some centered Gaussian density.
    
    

  • Wed 26 April, 2023. Aula 4, Palazzo Campana, 15:00-16:00
    Paolo Dai Pra (University of Verona)
    Title: Polarization and Coherence in Mean Field Games Driven by Private and Social Utility
    Abstract:  We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority (conformism) and the aspiration of sticking with the own type (stubbornness). We also consider a quadratic cost related to the rate at which a change in the state happens: changing opinion may be a costly operation. Depending on the parameters of the model, the game may have more than one Nash equilibrium, even though the corresponding N- player game does not. Moreover, it exhibits a very rich phase diagram, where polarized/unpolarized, coherent/incoherent equilibria may coexist, except for T small, where the equilibrium is always unique. We fully describe such phase diagram in closed form and provide a detailed numerical analysis of the N-player counterpart of the mean field game. 

Joint work with Marco Tolotti (Venezia) and Elena Sartori (Padova).

• • Wed 3 May, 2023. Aula 4, Palazzo Campana, 15:00-16:00
    Aleksandar Mijatovic (University of Warwick)
    Title: Title: Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function
    Abstract: We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non-increasing absolutely continuous function. We prove that the running time of our algorithm has finite exponential moments and provide bounds on its expected running time with explicit dependence on the characteristics of the process and the initial value of the function. The expected running time grows at most cubically in the stability parameter (as it approaches either $0$ or $1$) and is linear in the tempering parameter and the initial value of the function. Numerical performance, based on the implementation in the dedicated GitHub repository, exhibits a good agreement with our theoretical bounds. We provide numerical examples to illustrate the performance of our algorithm in Monte Carlo estimation. This is joint work with Jorge Ignacio Gonz\'alez C\'azares and Feng Lin.
      

  • Wed 10 May, 2023. Aula 4, Palazzo Campana,  15:00-16:00
    Luis Gil Alana (University of Navarra) 
    Title: Fractional integration and cointegration. An overview and recent developments
    Abstract:  In this talk we make a review of the concepts of fractional integration and cointegration. Both models belong to the category of long memory processes which are characterized because the spectral density function has one or more poles or singulatiries in the interval (0, pi). We focus on the cases where the singullarity occurs at the long run or zero frequency. We present various estimation procedures based non-parametric, semi-parametric and parametric methods, and an empirical applications is also conducted at the end of the talk.
    
    

  • Wed 24 May, 2023.  Aula 4, Palazzo Campana, 15:00-16:00
    Paolo Di Tella (University of Dresden)
    Title:  Enlargement of Filtrations, Martingale Representation and Related Control Problems
    Abstract:  In this talk we present some recent results about the propagation of martingale representation theorems to progressively enlarged filtrations. As an application we discuss some control problems under model uncertainty and in presence of an exogenous risk source.
    
    

  • Wed 31 May, 2023.  Aula 4, Palazzo Campana, 15:00-16:00
    Anna Paola Todino (Sapienza University of Rome)
    Title: Spherical Poisson Waves
    Abstract:  In this talk we discuss the universality of Gaussian behaviour for spherical Laplace eigenfunctions introducing a model of Poisson random waves in S^2. We study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity. We consider finite-dimensional distributions, harmonic coefficients and convergence in law in functional spaces, and we investigate carefully the interplay between the rates of divergence of eigenvalues and Poisson governing measures.
    The talk is based on a joint work with Solesne Bourguin, Claudio Durastanti and Domenico Marinucci.

• • Fri 23 June 2023.  Aula 4, Palazzo Campana, 14:30-15:30   --note the unusual time--
    Enrico Scalas (Sapienza University of Rome and University of Sussex)
    Title:  A fractional Hawkes process
    Abstract:   A Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables is introduced. This kernel decays as a power law with exponent $\beta+1 \in (1,2]$. Several analytical results are proved, in particular for the expected intensity of the point process and for the expected number of events of the counting process. These analytical results are used to validate algorithms that numerically invert the Laplace transform of the expected intensity as well as Monte Carlo simulations of the process. Finally, Monte Carlo simulations are used to derive the distribution of the number of events. The algorithms used for this presentation are available at https://github.com/habyarimanacassien/Fractional-Hawkes

Relevant papers
- Chen, J, Hawkes, A G and Scalas, E (2021) A fractional Hawkes process. In: Beghin, Luisa, Mainardi, Francesco and Garrappa, Roberto (eds.) Nonlocal and fractional operators. SEMA SIMAI Springer Series, 26 . Springer International Publishing, pp. 121-131.
- Habyarimana, Cassien, Aduda, Jane A, Scalas, Enrico, Chen, Jing, Hawkes, Alan G and Polito, Federico (2023) A fractional Hawkes process II: further characterization of the process. Physica A: Statistical Mechanics and its Applications, 615. pp. 1-11.

Past Talks:

First semester 2022/2023

• • Thu 24 Nov, 2022.  Aula 4, Palazzo Campana, 15:00-16:00
    Elisabetta Candellero (University of Roma Tre)
    Title: On the boundary at infinity for branching random walk
    Abstract:  We introduce an original connection between branching random walk on a graph and the Martin boundary for the underlying random walk. More precisely, we prove that when the graph is transient, supercritical branching random walk converges almost surely (under rescaling) to a random measure on the Martin boundary of the graph.
    This is based on a joint work with T. Hutchcroft (Caltech).
    
    

  • Thu 1 Dec, 2022.  Aula 4 and online, Palazzo Campana, 15:00-16:00
    Link: https://unito.webex.com/unito/j.php?MTID=m81c30bad50900bdd806bce104ab684a8
    Marta Pittavino (University of Geneve)
    Title: Is robust regression a suitable method to understand tax incentives for charitable giving? Case study from the Canton of Geneva, Switzerland
    Abstract: Under the current Swiss law, taxpayers can deduct charitable donations from their individual’s taxable income subject to a 20%-ceiling. This deductible ceiling was increased at the communal and cantonal level from a previous 5%-ceiling in 2009. The goal of the reform was boosting charitable giving to non-profit entities. However, the effects of this reform, and more generally of the existing Swiss system of tax deductions for charitable giving has never been empirically studied. The aim of this work is to provide as many taxation insights and deducters characteristics as possible into both the effects of the 2009 reform, as well as into the patterns of giving and deducting by different classes of deducters by income and wealth.
    Using unique panel data, shared by the Geneva Tax Administration, for a time framework of 11 years: 2001-2011, an in-depth statistical analysis was conducted. The overall taxpayer’s population has been described, dividing them into six categories according to the income distribution. We studied the changes in the volume of deductions between categories. Quantile regressions models for each year has been fitted to underlying the different income behaviors toward deductions. Moreover, a specific subset of deducters more sensitive to the deductible ceiling for their donations was identified and studied in detail. The overall net income, gross wealth, together with the year of birth, were the main covariates of interest. Standard linear regression and robust regression models were performed and significant variables, which help answering the questions of taxpayers’ charitable giving behavior, were identified.
    Income has resulted the most significant variable, driving donations, and robust regressions the statistical techniques better incorporating the data peculiarity, without giving too much weight to outliers, and with an excellent model fitting. This paper seeks to provide both Swiss and foreign academics and policymakers with new research and policy insights.
    Joint work with Giedre Lideikyte-Huber, Faculty of Law, Department of Commercial Law, Geneva, Center for Philanthropy, University of Geneva
    
    

  • Thu 15 Dec, 2022.  Sala S, Palazzo Campana, 15:00-16:00
    Bruno Toaldo (Universitá di Torino)
    Title:  Exit time of semi-Markov processes and the non-local heat equation on a time dependent domain
    Abstract: We introduce the theory of semi-Markov processes and their governing non-local (in time) equations. Then we focus on a non-local heat equation on a time-increasing parabolic set whose boundary is determined by a suitable curve. We provide a notion of solution for this equation and we study well-posedness under Dirichlet conditions outside the domain. A maximum principle is proved and used to derive uniqueness and continuity with respect to the initial datum of the solutions of the Dirichlet problem. Existence is proved by showing a stochastic representation based on the delayed Brownian motion killed on the boundary. (Joint work with G. Ascione and P. Patie)

Second semester 2021/2022

• • Tuesday 22 February, 2022.  Aula Lagrange, Palazzo Campana, 15:30-16:30
    Elena Bandini (University of Bologna)
    Title: Semimartingales with jumps, weak Dirichlet processes and generalized martingale problems
    Abstract: In this talk we will explain how the notion of weak Dirichlet process can be seen as the suitable generalization of the one of semimartingale with jumps. We will introduce the concept of characteristics for weak Dirichlet processes and provide a new unique decomposition for these processes, that holds for semimartingales as well. Then we will investigate a set of new useful chain rules and discuss a general framework of (possibly path-dependent with jumps) martingale problem.

• • Monday 4 April, 2022.  Aula Lagrange,  Palazzo Campana, 14:30-15:30
    Zivorad Tomovski  (University of Ostrava)
    Title: Fractional characteristic functions and fractional moments of random variables
    Abstract: In this talk we'll consider a fractional variant of the characteristic function of a random variable. It exists on the real whole line, where it is uniformly continous. We show that fractional moments can be expressed in terms of Riemann-Liouville integrals and derivatives of the fractional characteristic function. Fractional moments are of interest in particular for distributions whose integer moments do not exist. Some illustrative examples for fractional pdf's will be presented.

• • Wednesday 18 May, 2022.  Sala S,  Palazzo Campana. 14:30-15:30
    Enrico Scalas  (University of Sussex)
    Title: Time-fractional G/G/1 queues and applications to the double auction model
    Abstract:  We present some generalisations and limit theorems for the time-fractional G/G/1 queue, where arrivals and departures from the system come according to (independent) fractional Poisson processes. We then use some of these generalisations to develop and study a Fractional Double Auction model.

This is joint ongoing work with Jacob Butt and Nicos Georgiou. 

• • Wednesday 25 May, 2022.  Sala S,  Palazzo Campana. 14:30-15:30
    Luis Alberiko Gil-Alaña  (University of Navarra)
    Title:  Fractional Integration and Cointegration: An overview 

• • Wednesday 29 June, 2022.  Sala S and online. 14:30-15:30
    Lorenzo Torricelli  (University of Bologna)
    Title:  Continuous-time financial valuation: an overview with a focus on time changes
    Abstract:  We shortly review the foundations of the mathematical theory of no-arbitrage,  the classic option pricing models, and illustrate  some  approaches to valuation in relation to the observed market implied volatility surface. We discuss more in detail  exponential Lévy models and the time-changed approach, which finds wide application in modelling financial assets. Finally, some new perspectives and ideas are illustrated. 

First semester 2021/2022

• • Friday 1 October, 2021. Aula Magna, Palazzo Campana, Torino,17:00-18:00
    Francesco Russo (ENSTA Paris | Institut Polytechnique de Paris, France)
    Title: Fokker-Planck equations with terminal condition and related McKean probabilistic representation
    Abstract: Stochastic differential equations (SDEs) in the sense of McKean are stochastic differential equations, whose coefficients do not only depend on time and on the position of the solution process, but also on its marginal laws. Often they constitute probabilistic representation of conservative PDEs, called Fokker-Planck equations; In general Fokker-Planck PDEs are well-posed if the initial condition is specified. Here, alternatively, we consider the inverse problem which consists in prescribing the final data: in particular we give sufficient conditions for existence and uniqueness. We also provide a probabilistic representation of those PDEs in the form a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process. The research is motivated by some application consisting in representing some semilinear PDEs (typically Hamilton-Jacobi-Bellman in stochastic control) fully backwardly. This work is based on a collaboration with L. Izydorczyk (ENSTA), N. Oudhane (EDF), G. Tessitore (Milano Bicocca) 

• • Tuesday 09 November, 2021.   Aula 5, Palazzo Campana, Torino, 14:30-15:30
    Luisa Andreis  (University of Florence)
    Title: Phase transition in sparse random graphs and coagulation processes.
    Abstract: Inhomogeneous random graphs are a natural generalization of the well-known Erdős–Rényi random graph, where vertices are characterized by a type and edges are present independently according to the type of the vertices that they are connecting. In the sparse regime, these graphs undergo a phase transition in terms of the emergence of a giant component exactly as the classical Erdős–Rényi model. In this talk we will present an alternative approach, via large deviations, to prove this phase transition. This allows a comparison with the gelation phase transition that characterizes some coagulation process and with phase transitions of condensation type emerging in several systems of interacting components. 

This is an ongoing joint work with Wolfgang König (WIAS and TU Berlin), Tejas Iyer (WIAS),  Heide Langhammer (WIAS), Robert Patterson (WIAS).

• • Tuesday 30 November, 2021. Aula 5, Palazzo Campana, Torino,  14:30-15:30
    Alessandro Milazzo (Uppsala University, Sweden)
    Title:  Dynamic programming principle for classical and singular stochastic control with discretionary stopping
    Abstract: We prove the dynamic programming principle (DPP) for a class of problems where an agent controls a $d$-dimensional diffusive dynamics via both classical and singular controls and, moreover, is able to terminate the optimisation at a time of her choosing, prior to a given maturity. The time-horizon of the problem is random and it is the smallest between a fixed terminal time and the first exit time of the state dynamics from a Borel set. We consider both the cases in which the total available fuel for the singular control is either bounded or unbounded.
    We build upon existing proofs of DPP and extend results available in the traditional literature on singular control (e.g., Haussmann and Suo, SIAM J. Control Optim., 33, 1995) by relaxing some key assumptions and including the discretionary stopping feature. We also connect with more general versions of the DPP (e.g., Bouchard and Touzi, SIAM J. Control Optim., 49, 2011) by showing in detail how our class of problems meets the abstract requirements therein.
    
    This is a joint work with Tiziano De Angelis (University of Torino).
    
    

  • Tuesday 14 December 2021. Aula 5, Palazzo Campana, Torino, 14:30-15:30
    Cristina Costantini (University of Chieti-Pescara)
    Title:  Reflecting diffusions in nonsmooth domains: some new existence and uniqueness results.
    Abstract: Reflecting diffusions arise in many applications: from stochastic networks, to singular stochastic control, to the motion of physical particles, etc.. In many examples the domain in which the reflecting diffusion is to be confined is nonsmooth or the direction of reflection varies nonsmoothly: in these cases it is not obvious that a reflecting diffusion with the prescribed direction of reflection exists and is uniquely characterized. In fact only partial results are available.
    Most of the talk will focus on 2-dimensional domains. We will consider semimartingale reflecting diffusions, i.e. solutions of Stochastic Differential Equations with Reflection (SDERs), in piecewise smooth domains, possibly with cusps, with a varying direction of reflection on each ”side”. We will formulate an easily verifiable, geometrically  meaningful condition on the directions of reflection, under which existence and uniqueness of the solution to the SDER can be proved. In the case of a polygon with a constant direction of reflection on each side, this condition is also necessary: in this sense it is optimal.
    An outline of the proof will be given. The keystone of the proof is a new reverse ergodic theorem for nonhomogeneous, possibly killed, Markov chains. This is used in combination with existence of strong Markov solutions to SDERs, a coupling argument and rescaling arguments.
    Time permitting, some partial results in arbitrary dimension will also be presented.
    
    This is joint work with T.G. Kurtz (University of Wisconsin-Madison). 

Organized by

Tiziano De Angelis: tiziano.deangelis@unito.it 

Giuseppe D'Onofrio:  giuseppe.donofrio@unito.it

Elena Issoglio: elena.issoglio@unito.it