Random March 2019

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37 participants
53 discussions

An afternoon in Probability: Torino meets Leeds
by Elvira Di Nardo 24 Mar '19

24 Mar '19

%---------------------------------------------------------------------------% An afternoon in Probability: Torino meets Leeds Torino, April 16, 2019 %----------------------------------------------------------------------------% Room 09 - ESOMAS Department Corso Unione Sovietica 218/bis, 10134, Torino -----------------Program (Speakers and abstracts)------------------ 14:30-15:10 Tiziano De Angelis (School of Mathematics, University of Leeds) Title: Probabilistic results concerning smoothness of the value function and of the free boundary in optimal stopping Abstract: I will present probabilistic proofs of some regularity properties for the value function of general optimal stopping problems and for the associated optimal boundaries. In particular this talk focuses on C^1 regularity of the value function and Lipschitz continuity of the optimal boundary. Most of our arguments rely on fundamental concepts from the theory of Markov processes and bridge the probabilistic and the analytical strands of the literature on free boundary problems. I will also illustrate situations in which our work improves or complements known facts from PDE theory. 15:10-15:40 Elena Issoglio (School of Mathematics, University of Leeds) Title: A numerical scheme for a multidimensional SDEs with distributional drift Abstract: This talk focuses on a multidimensional SDE where the drift is an element of a fractional Sobolev space with negative order, hence a distribution. This SDE admits a unique weak solution in a suitable sense - this was proven in [Flandoli, Issoglio, Russo (2017)]. The aim here is to construct a numerical scheme to approximate this solution. One of the key problems is that the drift cannot be evaluated pointwise, hence we approximate it with suitable functions using Haar wavelets, and then apply (an extended version of) Euler-Maruyama scheme. We then show that the algorithm converges in law, and in the special 1-dimensional case we also get a rate of convergence. This talk is based on a joint work with T. De Angelis and M. Germain. 15.40-16:10 coffee break 16:10-16:50 Elena Vigna (ESOMAS , University of Leeds) Title: On time consistency for mean-variance portfolio selection Abstract: This talk addresses a comparison between different approaches to time inconsistency for the mean-variance portfolio selection problem. We define a suitable intertemporal preferences-driven reward and use it to compare the three possible approaches to time inconsistency for the mean-variance portfolio selection problem over $[t_0,T]$: precommitment approach, consistent planning or game theoretical approach, and dynamically optimal approach. We find that the precommitment strategy beats the other strategies if the investor only cares at the view point at time $t_0$ and is not concerned to be time-inconsistent in $(t_0,T)$; the consistent planning strategy dominates the dynamically optimal strategy until a time point $t^*\in(t_0,T)$ and is dominated by the dynamically optimal strategy from $t^*$ onwards. 16:50-17:30 Cristina Zucca (Dept. of Mathematics, University of Torino) Title: Inverse First Passage Time problem for diffusions Abstract: In several applications the dynamics of the variables of interest is described via suitable stochastic processes constrained by boundaries and the focus is on the first passage time (FPT). This is the direct FPT problem. However, there are also instances when the underlying stochastic process is assigned, one knows or estimates the FPT distribution and wishes to determine the corresponding boundary shape. This is the inverse first passage time (IFPT) problem. Here we study this problem in the case of one dimensional diffusion process constrained by a single boundary or two boundaries. We also extend the IFPT method to multivariate Gauss-Markov processes and we investigate the boundary shape corresponding to given FPT distributions for suitable choices of the parameters. Special attention is given to the Integrated Brownian motion and the two-dimensional Ornstein-Uhlenbeck process. Some examples of applications of the proposed methods will be illustrated. The participation is free. Please, share this information with people potentially interested. -- %------------------------------------------------------- Elvira Di Nardo Dept. Mathematics "G. Peano" University of Torino Via Carlo Alberto 10 10123 Torino, Italia tel. +39 0116702862 fax +39 0116702878 http://www.elviradinardo.it %------------------------------------------------------- <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_cam…> Mail priva di virus. www.avg.com <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_cam…> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>

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Seminari 25 marzo a Pisa
by Dario Trevisan 23 Mar '19

23 Mar '19

Cari tutti, lunedì 25 marzo presso la Sala Seminari del Dipartimento di Matematica dell'Università degli studi di Pisa si terranno i seguenti seminari: (Dear all, on Monday, March 25th, the following two talks will take place in Sala Seminari, Dipartimento di Matematica, University of Pisa:) ORE 14:00 -- Stefano Pagliarani (Università degli studi di Udine) **Contraction methods for a class of McKean-Vlasov (mean-field) SDEs with jumps.** ORE 15:00 -- Martin Saal (University of Darmstadt) **White noise solutions for (m)SQG** Tutti gli interessati sono invitati a partecipare. ### Abstract S. Pagliarani: We consider two prototype classes of McKean-Vlasov (mean-field) SDEs with jumps. In the first case, the coefficient is assumed to be affine in the state-variable, only measurable in the law, and the dynamics allow for Lévy jumps. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK-V SDE, and derive a discretized Picard iteration method that approximates the law of the solution. Numerical illustrations show the effectiveness of the method, which appears to be appropriate to handle multi-dimensional settings. We finally describe possible extensions and generalizations to more general settings. The second class of MKV SDEs that we consider allows for self-exicitng jumps, which amounts to having jumps through hitting the boundary in the equivalent large particle system. The corresponding PDE problem is a particular instance of free-boundary problems known as supercooled Stefan-like problems. We write a Volterra equation for the free boundary and prove contraction results that are useful to determine the properties of the solution and to provide convergent numerical schemes. Abstract M. Saal: The inviscid surface quasigeostrophic equation (SQG) describes (roughly speaking) the temperature in a rapidly rotating stratified fluid which is transported by the velocity field. The velocity field is connected to the temperature via Riesz-transform, which are singular integral operators. It has applications in both meteorological and oceanic flows, while in mathematics it is often used as a toy model for the 3D Euler equations due to some structural similarities of these equations. We give a brief overview on versions of the SQG equation and of the known mathematical results. For a modified version (mSQG) with a smoother velocity field, which links the SQG equation to the vorticity formulation of the 2D Euler equations, we will show that by using a special symmetry in the kernel a white noise solution to mSQG can be constructed. Finally, we give some comments on the difficulties of our approach in the case of SQG itself. -- Dario Trevisan, Università degli Studi di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 - Pisa (PI) Italy telephone: (+39) 050 2213832 mobile: (+39) 331 2899761 Skype: dario-trevisan e-mail: dario.trevisan AT unipi.it webpage: http://people.dm.unipi.it/trevisan/

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RTDA 13/D4 - Metodi matematici dell'economia e delle scienze attuariali e finanziarie
by Marco Scarsini 23 Mar '19

23 Mar '19

Bando Ricercatore art. 24, comma 3, lett. a) 13/D4 - Metodi matematici dell'economia e delle scienze attuariali e finanziarie Pubblicato sulla Gazzetta Ufficiale in data 15 marzo 2019 Settore scientifico-disciplinare SECS-S/06 - Metodi matematici dell'economia e delle scienze attuariali e finanziarie, presso il Dipartimento di Economia e Finanza della Luiss Libera Università Internazionale degli Studi Sociali Guido Carli. Codice concorso DEF-RIC-01/2019 Scadenza: 29 aprile 2019 - ore 14:00 Central European Summer Time (CEST) UTC+2 https://www.luiss.it/sites/www.luiss.it/files/Bando_7.pdf ******************************************************* Marco Scarsini Dipartimento di Economia e Finanza Luiss Viale Romania 32 00197 Roma, ITALY URL: http://docenti.luiss.it/scarsini/

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corso di dottorato a roma1
by Faggionato, Alessandra 23 Mar '19

23 Mar '19

Buongiorno Lunedì 1 aprile, ore 10:30-13:00, aula B, Dipartimento di Matematica La Sapienza ci sara' il primo incontro del corso di dottorato di Fabio Toninelli (in cui verra' anche stabilito l'orario definitivo). Il corso si svolgerà durante il mese di aprile. sotto trovate dettagli del corso. saluti alessandra faggionato %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fabio Toninelli (University Lyon 1) The dimer model: equilibrium and non-equilibrium aspects Abstract. This course focuses on various mathematical aspects of lattice dimer models. These are very classical two-dimensional statistical mechanics models, that are exactly solvable in some sense (Kasteleyn, 1961): partition function and correlations can be computed in determinantal form. Recently there has been a new wave of interest in dimer models, both in probability, combinatorics and mathematical physics. One reason is that these models, as well as other two-dimensional critical models, exhibit conformal invariance properties. Another interesting aspect is that they allow to obtain very nice Markov dynamics of two-dimensional interfaces, whose large-scale dynamical behavior can be studied. Detailed contents: • Kasteleyn theory (partition functions, correlations, determinantal properties) • correlations and representation determinantale • thermodynamic limit and ergodic Gibbs measures • height fluctuations and massless Gaussian field • dynamics of dimer models: mixing time and hydrodynamic limits. References : • R. Kenyon, Lectures on dimers, arXiv:0910.3129. • F. Toninelli, Lecture notes on the dimer model, http://math.univ-lyon1.fr/homes-www/toninelli/noteDimeri.pdf-- ************************************************* Prof. Alessandra Faggionato http://www1.mat.uniroma1.it/~faggionato/ Department of Mathematics University "La Sapienza" Piazzale Aldo Moro, 5 00185 - Rome Office 5, Phone (0039) 06 49913252 *************************************************

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TWELFTH EUROPEAN SUMMER SCHOOL IN FINANCIAL MATHEMATICS
by Tiziano Vargiolu 22 Mar '19

22 Mar '19

(please disregard the other message, this one is correct) We are pleased to announce the TWELFTHTH EUROPEAN SUMMER SCHOOL IN FINANCIAL MATHEMATICS that which will be held at the University of Padova, September 2 - 6, 2019. The European Summer School in Financial Mathematics aims at bringing together the most talented young researchers in the field, looking at the very young who only just started their PhD studies. The Summer School is centered around the two courses: - Gilles Pages, Benedikt Wilbertz: "Numerical Probability" - Mark Podolskij, Roberto Reno': "High Frequency Data" For schedule, registration and application for financial support, see: https://www.math.unipd.it/~vargiolu/ESSFM/ On behalf of the organizing committee Tiziano Vargiolu -------------------------------------------------------------------------- Tiziano Vargiolu Dipartimento di Matematica Phone: +39 049 8271383 Universita' di Padova Fax: +39 049 8271428 Via Trieste, 63 E-mail: vargiolu(a)math.unipd.it I-35121 Padova (Italy) WWW: http://www.math.unipd.it/~vargiolu --------------------------------------------------------------------------

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TWELFTH EUROPEAN SUMMER SCHOOL IN FINANCIAL MATHEMATICS
by Tiziano Vargiolu 22 Mar '19

22 Mar '19

We are pleased to announce the TWELFTHTH EUROPEAN SUMMER SCHOOL IN FINANCIAL MATHEMATICS that which will be held in Vienna, University of Padova, September 2 - 6, 2019. The European Summer School in Financial Mathematics aims at bringing together the most talented young researchers in the field, looking at the very young who only just started their PhD studies. The Summer School is centered around the two courses: - Gilles Pages, Benedikt Wilbertz: "Numerical Probability" - Mark Podolskij, Roberto Reno': "High Frequency Data" For schedule, registration and application for financial support, see: https://www.math.unipd.it/~vargiolu/ESSFM/ On behalf of the organizing committee Tiziano Vargiolu -------------------------------------------------------------------------- Tiziano Vargiolu Dipartimento di Matematica Phone: +39 049 8271383 Universita' di Padova Fax: +39 049 8271428 Via Trieste, 63 E-mail: vargiolu(a)math.unipd.it I-35121 Padova (Italy) WWW: http://www.math.unipd.it/~vargiolu --------------------------------------------------------------------------

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Seminar announcement
by Marco Scarsini 22 Mar '19

22 Mar '19

Thursday, 28 March, 12:00 Room 204 Luiss Viale Romania, 32 00197 Roma Paul Dütting, London School of Economics and Political Science Prophet inequalities for independent random variables from an unknown distribution Abstract: A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: Given a sequence of random variables X_1,…,X_n drawn independently from a distribution F, the goal is to choose a stopping time τ so as to maximize α such that for all distributions F we have E[X_τ] ≥ α⋅E[max_t X_t]. What makes this problem challenging is that the decision whether τ = t may only depend on the values of the random variables X_1,…,X_t and on the distribution F. For quite some time the best known bound for the problem was α ≥ 1−1/e ≈ 0.632 [Hill and Kertz, 1982]. Only recently this bound was improved by Abolhassani et al. [2017], and a tight bound of α ≈ 0.745 was obtained by Correa et al. [2017]. The case where F is unknown, such that the decision whether τ = t may depend only on the values of the first t random variables but not on F, is equally well motivated (e.g., [Azar et al., 2014]) but has received much less attention. A straightforward guarantee for this case of α ≥ 1/e ≈ 0.368 can be derived from the solution to the secretary problem. Our main result is that this bound is tight. Motivated by this impossibility result we investigate the case where the stopping time may additionally depend on a limited number of samples from F. An extension of our main result shows that even with o(n) samples α ≤ 1/e, so that the interesting case is the one with Ω(n) samples. Here we show that n samples allow for a significant improvement over the secretary problem, while O(n^2) samples are equivalent to knowledge of the distribution: specifically, with n samples α ≥ 1−1/e ≈ 0.632 and α ≤ ln(2) ≈ 0.693, and with O(n^2) samples α ≥ 0.745−ε for any ε > 0. Joint work with Jose R. Correa, Felix Fischer, and Kevin Schewior Preprint: https://arxiv.org/abs/1811.06114 The calendar of future seminars can be found at http://economiaefinanza.luiss.it/en/seminari/prossimi-seminari ******************************************************* Marco Scarsini Dipartimento di Economia e Finanza Luiss Viale Romania 32 00197 Roma, ITALY URL: http://docenti.luiss.it/scarsini/

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Mini-course announcement: Affine and polynomial processes with applications in Finance [Dept. Comp. Science - UniVr]
by Luca di persio 22 Mar '19

22 Mar '19

The Dept. of Comp. Science, College of Mathematics [ UniVr ], will host the following mini-course *Title*: Affine and polynomial processes with applications in Finance which will be given by prof. Christa Cuchiero *Abstract*: The course will be focused on the analysis of affine and polynomial processes. Particular emphasis will be given to the study of their infinite dimensional versions, which take values in (signed) measures or functions spaces. This allows to consider applications ranging from rough volatility models over non-linear PDEs, to stochastic portfolio theory. *Time table*: Monday 25/03: 9.30 -11.30 (Room G) Wednesday 27/03: 13.30-16.30 (Room M) Thursday 28/03: 12.30 - 14.30 ( Room Tessari) See also: http://www.di.univr.it/?ent=seminario&id=4703 Do not hesitate to contact me: luca.dipersio(a)univr.it for any further info. Best, LuCa __ Luca Di Persio - PhD College of Mathematics Dept. of Computer Science - University of Verona strada le Grazie 15 - 37134 Verona - Italy Tel : +39 045 802 7968 <http://www.hpa8.com/>

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Conference in Verona
by Stefania Ugolini 21 Mar '19

21 Mar '19

The Department of Mathematics of the University of Milano in collaboration with INDAM-GNAMPA, University of Trento, University of Insubria, Linneaus University, Wuppertal University organizes the following conference: RANDOM TRANSFORMATIONS AND INVARIANCE INSTOCHASTIC DYNAMICS Chapter Hall of San Giorgio in Braida’smonastery, Verona 25-29 March 2019 The study of transformations, symmetries and invariance properties of ordinary and partial differential equations, and associated conserved quantities, is a classical area of research. The inclusion of random terms in the deterministic systems has received a considerable attention only in recent years. The purpose of the conference is to allow researchers of different areas, particularly mathematical physics, probability, analysis, interact in order to reduce the gap between deterministic and stochastic frameworks. For further information see http://users.mat.unimi.it/users/ugolini/workshop2019/ On behalf of the organizing committe, Stefania Ugolini. <signaturebeforequotedtext></signaturebeforequotedtext><signatureafterquotedtext></signatureafterquotedtext>

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de Finetti risk seminar
by Emanuela Rosazza 21 Mar '19

21 Mar '19

Gentile Prof. Cambini, Le sarei grata se potesse inoltrare il seguente avviso di messaggio. La ringrazio anticipatamente e saluto cordialmente, Emanuela --- On behalf of the Scientific Committee of the de Finetti Risk Seminars, we are glad to invite you to participate at the following Lecture A mathematical model of learning reward uncertainty in the brain Rafal Bogacz Nuffield Department of Clinical Neurosciences, University of Oxford Abstract: To maximise their chances for survival, humans and animals need to base their decisions not only on the average consequences of chosen actions, but also on the variability of the rewards resulting from these actions. For example, when ones food reserves are depleted, one should prefer to forage in an area where food is guaranteed, rather than an area where the amount of food is higher on average but variable, thus avoiding the risk of starvation. To implement such policies, the brain needs to be able to learn about variability of rewards resulting from taking different actions. This talk will present a simple mathematical model describing how such learning may be implemented in the brain. The models suggests how the information about reward uncertainty is used by the brain to make decisions that not only maximize expected rewards but also take risks into account. The models is consistent with a wide range of experimental data from neuroscience. The talk will also include a discussion of the relationship between the model and the probability weighting functions from the prospect theory. LOCATION: The seminar will be held on Wednesday, March 27, at 15.00 at room 3-E4-SR03, Bocconi University, Via Rontgen 1, 3rd floor, Milano. A refreshment will be offered at 14.45. Scientific Committee: Prof. Simone Cerreia-Vioglio (Univ. Bocconi) Prof. Marco Frittelli (Univ. degli Studi di Milano) Prof. Fabio Maccheroni (Univ. Bocconi) Prof. Massimo Marinacci (Univ. Bocconi) Prof. Emanuela Rosazza Gianin (Univ. Milano-Bicocca) Dott. Marco Maggis (Univ. degli Studi di Milano) ******************************************************************************************* Emanuela Rosazza Gianin Dipartimento di Statistica e Metodi Quantitativi Università di Milano-Bicocca Edificio U7 – 4° Piano Via Bicocca degli Arcimboldi, 8 20126 Milano Tel. 02 64483208 Fax. 02 64483105 e-mail: emanuela.rosazza1(a)unimib.it *******************************************************************************************

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