- Random - Mailing list — Dipartimento di Matematica, UniPI

Mini course in Verona - Simone Mattia Scotti: Real markets, microstructure, clusters and Hawkes with a Branching process point of view.
by Luca di persio 20 Feb '17

20 Feb '17

*Mini course announcement* Prof. Simone Mattia Scotti [ LPMA, Université Paris Diderot ] will give a mini course on *Real markets, microstructure, clusters and Hawkes with a Branching process point of view*, according with the following time table: 21st of March (2017) : Room I 1430-1730 23rd of March (2017) : Room M 1530-1730 24th of March (2017) : Room M 1430-1730 all the lessons will take place at the Dept. of Computer Science - UniVr Strada le Grazie, 15 - Verona Ca' Vignal located here https://goo.gl/maps/Yx2JU *Abstract and structure of the course* The analysis of real financial markets, along with the study of related economic time series, represents an increasing field of research and development of effective applications, from the stochastic processes point of views, as well as from the statistic and computational sides of the moon. In this mini-course, we first recall the classical framework behind the modern and mathematically rigorous, theory of finance, starting from the treatment of continuous-path stochastic processes. Then, we focus on the microstructure of market data, discussing both limit and market orders, along with correlated liquidity problems. In a second part, we will specialize our analysis on a particular feature of financial markets, namely the existence of jumps' cluster. It is worth to mention that the latter has been highlighted in recent literature in microstructure, showing to have a deep impact on real markets and representing a main research axis in the field. >From a mathematical point-of-view, we will first introduce point processes and then Hawkes processes. We will show that the self-exciting structure of Hawkes processes can easily explain some features exhibited by financial data, e.g. the cluster effects. In the third part, we will introduce the branching processes (CBI) showing that they can be seen as a natural extension (marked versions) of Hawkes processes. We will show that this class of models has very nice properties from computational as well as from analytical point of view, particularly by exploiting the Dawson-Li representation. Moreover, we will point out some unexpected features of the aforementioned approaches, such, e.g., the persistency of low interest rates and negative risk premium in electricity markets. A detailed bibliograpy will be given during the course. ___________ Do not hesitate to contact me for further details: luca.dipersio(a)univr.it LuCa -- __ Luca Di Persio - PhD assistant professor of Probability and Mathematical Finance Dept. Informatics University of Verona strada le Grazie 15 - 37134 Verona - Italy Tel : +39 045 802 7968 <+39%20045%20802%207968> Dept. Math University of Trento V. Sommarive, 14 - 38123 Povo - Italy Tel : +39 0461 281686 <+39%200461%20281686>

1 0

Mini course in Verona - Adrian Zalinescu : Introduction to SPDEs with applications
by Luca di persio 18 Feb '17

18 Feb '17

*Mini course announcement* Prof. Adrian Zalinescu [ Universitatea Alexandru Ioan Cuza - Iaşi, Romania ] will give a mini course on *Introduction to Stochastic Partial Di fferential Equations* (with applications to Finance, Biology, etc.), according with the following calendar 13 - 20 - 27 of March (2017) time table: from 1430 to 1730 all the lessons will take place at the Dept. of Computer Science - UniVr Strada le Grazie, 15 - Verona Ca' Vignal 2, first floor , *Room M* located here https://goo.gl/maps/Yx2JU The* tentative programme* is the following: 1. *Gaussian measure theory* Random vectors and Bochner integral. Some elements of probability in in nite-dimensional spaces are considered, with emphasis on the integration of random vectors with values in separable Banach-spaces and in operator spaces. Gaussian measures. We introduce cylindrical Gaussian random variables and Hilbert-spacevalued Gaussian random variables and then de ne cylindrical Wiener processes and Q-Wiener processes (i.e. with the covariance given by the trace-class operator Q) in a natural way. Stochastic integral and Ito's formula. The stochastic integral is constructed with respect to a cylindrical Wiener process, then with respect to a Q-Wiener process, by extending the integral of elementary processes. Some properties of the stochastic integral are given, including Ito's formula. 2. *Stochastic Di erential Equations* Semigroup Theory. In this section we review the fundamentals of semigroup theory. Stochastic Convolutions and Linear SPDEs. We derive existence and uniqueness of di erent types of solutions for linear SDEs driven by generators of C0-semigroups. The method is based on the study of the stochastic convolution. Solutions by Variational Method. The purpose is to study solutions of nonlinear SPDEs, which are seen as evolution equations in a Gelfand triplet, under assumptions of compact embedding or monotone coe cients. 3. *Applications* Along the abstract study of SDEs in in nite-dimensional spaces, various examples of SPDEs with applications in physics, biology and mathematical finance will be given. A detailed bibliograpy will be given during the course. ___________ Do not hesitate to contact me for further details: luca.dipersio(a)univr.it LuCa __ Luca Di Persio - PhD assistant professor of Probability and Mathematical Finance Dept. Informatics University of Verona strada le Grazie 15 - 37134 Verona - Italy Tel : +39 045 802 7968 Dept. Math University of Trento V. Sommarive, 14 - 38123 Povo - Italy Tel : +39 0461 281686

1 0

Seminar announcement
by Marco Scarsini 17 Feb '17

17 Feb '17

Thursday 23 February from 12.00 to 13.00 LUISS room 207 viale Romania 32 00197 Roma. *Speaker:* Bruno Ziliotto (CNRS) *Title:* In zero-sum stochastic games, the payoff is constant *Abstract*: In a zero-sum stochastic game, at each stage, two adversary players take decisions and receive a stage payoff determined by these actions and by a random variable called state of nature. The total payoff is the discounted sum of the stage payoffs. Assume that players are very patient and use optimal strategies. We then prove that at any point in the game, players get essentially the same payoff: the payoff is constant. No game theory prerequisite of any kind is needed to understand this talk. (joint work with Miquel Oliu Barton) ******************************************************* Marco Scarsini Dipartimento di Economia e Finanza LUISS Viale Romania 32 00197 Roma, ITALY URL: http://docenti.luiss.it/scarsini/

1 0

Seminario CARLO SGARRA @ UniTo
by Federico Polito 17 Feb '17

17 Feb '17

********************************************************************* SEMINARI DI PROBABILITA' E STATISTICA MATEMATICA DIPARTIMENTO DI MATEMATICA "G. PEANO" UNIVERSITA' DEGLI STUDI DI TORINO ********************************************************************* mercoledì 15 Marzo 2017 alle ore 11:30 in Aula C presso il Dipartimento di Matematica "G. Peano" dell'Università degli Studi di Torino, Via Carlo Alberto 10, Il Prof. CARLO SGARRA (Politecnico di Milano) terrà un seminario dal titolo A BRANCHING PROCESS-BASED APPROACH TO POWER MARKETS (The talk will be mainly based on a joint paper with Y. Jiao, C. Ma and S. Scotti). Abstract: Energy markets, and in particular, electricity markets, exhibit very peculiar features. The historical series of both futures and spot prices include seasonality, mean-reversion, spikes and small fluctuations. Very often a stochastic volatility dynamics is postulated in order to explain their high degree of variability. After the pioneering paper by Schwartz, where an Ornstein-Uhlenbeck dynamics is assumed to describe the spot price behavior, several different approaches have been investigated in order to describe the price evolution. High frequency trading, on the other hand, introduced some new features in commodity prices dynamics: in a recent paper by V. Filimonov, D. Bicchetti, N. Maystre and D. Sornette evidence is shown of endogeneity and structural regime shift, and in order to quantify this level the branching ratio is adopted as a measure of this endogenous impact and a Hawkes processes dynamics is assumed as a reasonable modelling framework taking into account the self-exciting properties. The purpose of the present investigation is to propose a new modeling framework including all the above mentioned features, still keeping a high level of tractability. The model considered allows to obtain the most common derivatives prices in closed or semi-closed form. Here with semi-closed we mean that the Laplace transform of the derivative price admits an explicit expression. The models we are going to introduce can describe the prices dynamics in two different forms, that can be proved to be equivalent: the first is a representation based on random fields, the second is based on Continuous Branching Processes with Immigration (CBI in the following). Tutti gli interessati sono invitati a partecipare. -- Federico Polito Department of Mathematics University of Torino Via Carlo Alberto, 10 10123, Torino, Italy Email: federico.polito(a)unito.it Tel: +39 011 6702862 Web: www.fpolito.eu

1 0

seminario Matteo Burzoni in Bicocca
by Fabio Bellini 17 Feb '17

17 Feb '17

1 0

Teaching assistantships at LUISS
by Marco Scarsini 16 Feb '17

16 Feb '17

LUISS is looking for teaching assistants for various courses in mathematics, statistics, and computer science for the academic year 2017/2018. Teaching assistants are expected to teach in either English or Italian (not necessarily both), hold office hours, and assist with exams. Whoever is interested should fill out the application form that can be found at the pages http://www.luiss.edu/ateneo/opportunita-di-lavoro/reclutamento-docenti-cont… (Department of Economics and Finance), http://www.luiss.edu/ateneo/opportunita-di-lavoro/reclutamento-docenti-cont… (Department of Management). The deadline is 02 March 2017. I would greatly appreciate if you could inform your graduate students of this opportunity. ******************************************************* Marco Scarsini Dipartimento di Economia e Finanza LUISS Viale Romania 32 00197 Roma, ITALY URL: http://docenti.luiss.it/scarsini/

1 0

Annuncio di seminari
by Piccioni, Mauro 15 Feb '17

15 Feb '17

Il giorno 21 febbraio 2017 presso l'Aula E del Dipartimento di Matematica, Sapienza Università di Roma si terranno i seguenti seminari di Probabilità e Statistica Matematica: Ore 14.30 Wolfgand Woess (TU Graz, Austria) Multidimensional reflected random walk - some results and many questions Abstract: Let (Y_n,V_n) be i.i.d. distributed, with the components r and s-dimensional, respectively. Reﬂected random walk starting at a point x of the positive r-dimensional orthant is deﬁned recursively by X_0 = x, X_n = |X_{n−1}−Y_n|, where |(a_1,...,a_r)| = (|a_1|,...,|a_r|). In R^s, consider the ordinary sum S_n = V_1 +···+V_n . We are interested in (topological) recurrence of the process (X_n,v+S_n) starting at (x,v). While this is quite well understood for refelcted random walk with r=1, in higher dimension (r \geq 2) or with some non-reﬂected coordinates (s \in {1,2}) we have a few basic results and various open questions with some partial answers. This is work with Judith Kloas, with input from Marc Peigne' and Wojciech Cygan. Ore 15.30 Oriane Blondel (CNRS Lyon, France) More random walks on random walks Abstract: We consider a Poissonian distribution of particles performing independent simple random walks. Simultaneously, on top of this system, a random walker evolves with a drift to the right when it is on top of (at least) a particle, to the left when it is on an empty site. We obtain a LLN, CLT and large deviation bounds in high and low density. Joint work with Marcelo Hilario, Renato dos Santos, Vladas Sidoravicius, Augusto Teixeira. Tutti gli interessati sono invitati a partecipare. per informazioni rivolgersi a piccioni(a)mat.uniroma1.it

1 0

Seminario Prof. Giorgio Ferrari
by Tiziano Vargiolu 15 Feb '17

15 Feb '17

Il giorno martedi' 21 febbraio alle ore 11 presso il Dipartimento di Matematica dell'Universita' di Padova, via Trieste 63, aula 1AD/100, il prof. Giorgio Ferrari dell'Universita' di Bielefeld, e ospite del Dipartimento di Matematica in qualita' di professore visitatore nell'ambito del progetto YITP (Young Investigation Training Program), terra' un seminario dal titolo Controlling Public Debt without forgetting Inflation Abstract -------- Consider a government that wants to control its debt-to-GDP (gross domestic product) ratio, while taking into consideration the evolution of the inflation rate of the country. The uncontrolled inflation rate follows an Ornstein-Uhlenbeck dynamics and affects the growth rate of the debt ratio. The level of the latter can be reduced by the government through fiscal interventions. The government aims at choosing a debt reduction policy which minimises the total expected cost of having debt, plus the total expected cost of interventions on debt ratio. We model such problem as a two-dimensional singular stochastic control problem over an infinite time-horizon. We show that it is optimal for the government to adopt a policy that keeps the debt-to-GDP ratio under an inflation-dependent ceiling. This curve is the free-boundary of an associated fully two-dimensional optimal stopping problem, and it is shown to be the unique solution of a nonlinear integral equation. Finally, some economic conclusions are drawn. Tutti gli interessati sono invitati a partecipare. Tiziano -------------------------------------------------------------------------- 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 --------------------------------------------------------------------------

1 0

BISP10, Milano, June 2017-extended deadlines
by fabrizio＠mi.imati.cnr.it 15 Feb '17

15 Feb '17

The 10th workshop on Bayesian Inference for Stochastic Processes (BISP10) will take place in Milano, Italy, on June 13-15, 2017. ** The online abstract submission (for oral or poster presentation) is extended to the 28th of February ** Theoretical and applied contributions on Bayesian inference in stochastic processes are both welcome. A non-exhaustive list of topics includes Markov processes, temporal and spatial processes, computations and methods for complex structures, empirical processes, birth-death and branching processes, networks and relational data, queuing, signal processes, stochastic differential equations. BISP10 is dedicated to Pietro Muliere, on his 70th birthday. All information can be found on the website : www.unibocconi.eu/bisp10 If you have any questions, please contact the Chairs of the Local and Scientific Committees: Sonia Petrone sonia.petrone(a)unibocconi.it and Fabrizio Ruggeri fabrizio(a)mi.imati.cnr.it Best wishes, and we look forward to welcoming you in Milano at BISP10. Sonia Petrone & Fabrizio Ruggeri -- Fabrizio Ruggeri fabrizio AT mi.imati.cnr.it CNR IMATI tel +39 0223699532 Via Bassini 15 fax +39 0223699538 I-20133 Milano (Italy) web.mi.imati.cnr.it/fabrizio

1 0

Seminario Dott.ssa Zehra Eksi
by Katia Colaneri 14 Feb '17

14 Feb '17

Il giorno giovedì 16 febbraio alle ore 16 presso il Dipartimento di Economia dell'Università di Perugia, la Dott.ssa Zehra Eksi, Assistant Professor presso la WU-Vienna University of Economics and Business, e ospite del Dipartimento di Economia in qualità di professore visitatore nell'ambito del progetto YITP (Young Investigation Training Program), terrà un seminario dal titolo "EM Algorithm for Markov Chains observed via Gaussian Noise and Point Processes Information" *Abstract*: In this paper we obtain an Expectation-Maximization (EM) algorithm for a setting in which the state variable follows a finite-state Markov chain observed via diffusive and point process information. Such a setting may arise, for example, in the modelling of sovereign credit risk where information stems from default history (jump component) and CDS spreads (diffusive component). Obtaining the EM algorithm amounts to the derivation of finite-dimensional filters for quantities such as number of jumps and sojourn times associated to the Markov chain. In this context, we obtain both exact and unnormalized filters for the related quantities. Moreover, we compute discretized robust versions of the unnormalized filters. Next, we introduce a novel goodness of fit test to check how well the estimated model explains a given data set. Finally, we run a simulation study to test speed and accuracy of the algorithm. In particular, we provide a comparison for the estimates resulting from the robust and naive discretization and the value of point process information (This is a Joint work with Camilla Damian and Ruediger Frey) Tutti gli interessati sono invitati a partecipare. Dott.ssa Katia Colaneri Department of Economics, University of Perugia Via A. Pascoli 20, Perugia 06123- Italy e-mail: katia.colaneri@unipg <katia.colaneri(a)gmail.com>.it

1 0