Vai al contenuto principale

PhD Projects (deadline: tba)

The following PhD projects are part of a call for 2+1 fully funded PhD scholarships in the framework of the PhD in Modeling and Data Science  at the University of Turin (Italy) (one scholarship is reserved to the project founded by Hub Editoriale, the last one in the list below).

The PhD program is interdisciplinary, and it involves branches of mathematics, informatics, economics, statistics, and physics.

The scholarship is for three years, starting from 1st February 2023.

Call for Applications.

All interested candidates should submit their application online via this link 

Deadline for applying is 17 November 2022 at 12:00pm. Notice that the application requires two reference letters, which should be submitted via the same link by the referees before the application deadline. The referees will be able to submit their letters only after the candidate has input all the required information and closed their (part of the) application. If the letters are not submitted by the deadline the application will not be valid.

More information, including the official call and all relevant deadlines, can also be found here 
https://www.dottorato.unito.it/do/home.pl/View?doc=2_tornata_XXXVIII_ciclo_e_PNRR.html

Abstract

Multi-asset derivative pricing is still an active field of research in financial modeling, calling for multivariate stochastic models that reproduce well-known stylized facts such as skewness and excess kurtosis of marginal return distributions.

The objectives of this research project are to build stochastic models for financial assets, develop calibration procedures and simulation methods. Simulations are necessary to price derivatives if analytical pricing formulas are not available, and they are also necessary to generate future scenarios for out-of-sample evaluation.

A class of models widely used in finance are Markov processes. Among them, Lévy processes, which are characterized by independent and time-homogeneous increments, are widely used because of their analytical tractability and good fit on financial data. These processes are recently used to build multivariate models able to incorporate linear and non-linear dependencies among assets. In fact, both linear and non-linear dependence may affect the price of a multi-asset derivative or the risk associated with a financial position.

One of the objectives of the present project is to build and characterize multivariate stochastic processes able to reproduce well-known stylized facts and with a flexible dependence structure. A way to build multivariate stochastic models in finance is to subordinate a Lévy process or, more in general, a Markov process.

Subordination has the nice economic interpretation of a change of time. The underlying idea is that the time runs fast when there are a lot of orders, while it slows down when trade is stale. If both the processes are of Lèvy type the resulting process is also Lèvy, otherwise we introduce time inhomogeneity using more general change of time.

Once the model has been built the objective becomes to calibrate the models on real data, and evaluate its fit properties.

Supervisors: Prof. Elvira Di Nardo, Prof. Patrizia Semeraro

This project will be carried out in the Department of Mathematics at the University of Turin (Italy). For more information, do not hesitate to contact the supervisors. 

Abstract

Supervisor: Prof. Marco Maggiora

 

Abstract

The project aims at developing methods and tools for digital twins, i.e. a digital replica of a living or nonliving physical entity (i.e., "the system") that allows us to simulate the effects of a natural event or human intervention on the system itself. Digital twins are workflows of modular, composable, portable, scalable cloud services embedding high-performance simulations, AI-based data analysis stages and possibly specialized Quantum kernels. The project will extend the Common Workflow Language (CWL) open standard and its Streamflow implementation to match the need of future generation digital twins.

Supervisor: Prof. Marco Aldinucci

This project will be carried out in the Department of Computer Science at the University of Turin (Italy). For more information, do not hesitate to contact the supervisor.

Abstract

Quantum Computing is a promising and emerging technology with revolutionary potential in the high-performance computing landscape. At the dawn of the Quantum era, we still miss a complete theory of quantum computability, i.e., which problem can be solved and which can be solved better than what is already possible according to Turing's computability. According to state-of-the-art and in the medium term, we expect to use Quantum Systems as accelerators to solve a narrow class of computing problems. Accelerators must be coupled and integrated into traditional HPC systems (clusters of multicores with GPUs). With the installation of the first 6 European Quantum machines expected in 2024-25 (one of them in CINECA - Italy), the integration of Quantum Computing and HPC is already an urgent open problem. We expect the first successful integration to happen with loosely coupled processes, such as scientific workflows where some phases of the computation (not all of them) are accelerated.  A viable method relies on modern workflow systems like the StreamFlow WMS. They aim to build complex pipelines by the composition of fully segregated modules that can be independently deployed onto different, possibly heterogeneous, platforms. Modules are assembled according to true data dependency relations, separated by deployment indications. This has several advantages against traditional kernel invocation happening within the application business code, for example, in GPU accelerators. 1) Modules does not need to be compiled together; different module might live in very different software stacks.  2) Data movement can be semi-automatically marshaled/unmarshalled encrypted/decrypted (via "data-mover") to match the different encoding of data in different systems; data-movers can also serve for in-situ/in-transit computing, that is, this case the transcoding of the problem from traditional to QC terms and vice-versa. The full automatization of this transcoding problem is an open problem in itself, and in early-stage experimentation, it can be helpful to facilitate the hand-coding of the transcoding rather than attempting to make it fully automatic. 3) The independence of different modules guarantees portability and rapid prototyping; it should be possible to quickly test a module in a simulator and run it on a real machine without recoding the application.

Supervisor: Prof. Marco Aldinucci

This project will be carried out in the Department of Computer Science in joint with the Department of Physics at the University of Turin (Italy). For more information, do not hesitate to contact the supervisor.

Abstract

This project intends to address the issue of accessibility to scientific information contained in graphic structures for people with visual disabilities. Today’s assistive technologies provide a number of tools to support visually impaired people, however these technologies often present severe limitations in non strictly textual contexts. In fact, scientific texts very often contain "structured" graphic information such as tables or diagrams representing large amounts of structured data usually employed in scientific analysis. The idea behind this project is to use Natural Language Processing and in particular conversational interfaces technologies to allow visually impaired people to navigate scientific diagrams towards a conversation with a chatbot.

Supervisor: Prof. Luca Anselma

This project will be carried out in the Department of Computer Science at the University of Turin (Italy). For more information, do not hesitate to contact the supervisor.

Abstract

A stochastic interacting particle system is a system of particles (also known as agents) whose stochastic dynamics is dependent on the other particles. This system of stochastic equations describes the interactions between the particles at the microscopic level. Interacting particle systems find applications in many fields, such as biology (herds), sociology (herding behaviour), energy markets (price formation), etc. The drawback of this description is the complexity of the model, however it is known that, under suitable conditions, if we let the number of particles tend to infinity, then the (infinite) system will converge, in a suitable sense, to a partial differential equation known as Fokker-Planck equation. This limiting procedure is known as ''propagation of chaos''. The limiting equation corresponds to the macroscopic description of the stochastic system and it is much less complex (being a single equation instead of a large system), at least from a computational point of view.

This PhD project will focus on the study of stochastic interacting particle systems with singular coefficients, for example when the drift of each particle dynamics is highly non smooth. Singular coefficients would account for the singular nature of the dynamics of each particle, that could be due to exogenous factors (the environment) or endogenous ones (the particles themselves). In this specific framework, we will investigate the limit as the number of particles tends to infinity and prove a propagation of chaos result, hence establish the link between the microscopic and the macroscopic view. Afterwards, we will add a control variable to the system and/or to the limit partial differential equation. In terms of modelling, adding a control variable amounts to allow each particle (or agent) to modify its dynamics, for example changing the drift, upon paying a cost. The aim of each agent is to optimize their dynamics and at the same time minimize their cost. Thus this problem becomes a stochastic optimization problem with a large number of agents with singular and stochastic dynamics, which is the microscopic view. The corresponding macroscopic view is conjectured to be a controlled Fokker-Planck equation with singular coefficients. Our aim will be to formalize this mathematically and establish the propagation of chaos result in this more involved setting.

We observe that this mathematical formulation opens the door to many applications, especially with the help of data science and deep learning algorithms. Indeed, when the number of particles is large and/or the dimension of the underlying space is large, then fitting this model to real data becomes a data science problem. One possible tool that could be used to fit this high-dimensional model would be deep learning. Using this, one could investigate numerically the goodness of the approximation of the particle system with its limit equation, i.e. check the validity of the propagation of chaos result in real-life examples. This however will not be part of the current PhD project and it is left as future work after the completion of this PhD project.

Supervisors: Prof. Elena Issoglio, Prof. Francesco Russo

Prof Russo is Professor in Mathematics of `class Expetionelle' at ENSTA Paris Tech in France. Dr Issoglio is a faculty member in mathematics at the University of Turin. A co-tutorship between Torino and Paris will be formalized for this project aiming to release of the double title between the two universities. The student will likely spend 1.5 years in Turin and 1.5 years in Paris. For more information, do not hesitate to contact the supervisors.

Abstract

Many socio-economical critical human-centered domains (such as sustainability, public health, emergency management) are characterized by highly complex and dynamic systems, requiring data analysis techniques to support decision making. These challenges require obtaining a deeper understanding of complex relationships and interactions among a diverse spectrum of entities in different evolving contexts. The goal of this project is to develop techniques to mine causality relationships among different aspects of the complex systems under study, and to investigate how existing data analysis techniques can be tuned and revised to benefit from the available knowledge about such causality relationships among different aspects of the systems under analysis.

Supervisor: Prof. Maria Luisa Sapino

This project will be carried out in the Department of Computer Science at the University of Turin (Italy). For more information, do not hesitate to contact the supervisor.

Last update: 20/10/2022 14:18
Non cliccare qui!