The doctorate is one of the programmes of the INdAM-DP-COFUND-2015.
We offer a variety of research related courses as well as introductory level courses which help first-year students strengthen their mathematical background.
At the beginning of every academic year, in consultation with their tutor, students present a study plan to the doctorate council where they specify what research and training they plan to do in the coming academic year. In the three years of the program, students are expected to participate in seminars offered by the school and to take part in research internships in institutions both in and outside Italy.
At the end of each academic year, with the exception of the final year, the students will then be interviewed on the studies and research they have carried out during the year in front of a committee appointed by the doctorate council. Successfully passing this interview means that the students can keep their post and fellowship, and thus be admitted to the following year. At the interview, the students will present a report on their scholarly activity, their research and its results, seminars, congresses, or other scientific activities they have participated in, and any publications they have produced. For the admission into the final year, this report will include a section relating to the progress made in their research project.
The program is in strict collaboration with the international Ph.D. school Gran Sasso Science Institute (GSSI, L'Aquila) and the students will have the possibility to follow all the activities held at the GSSI. Our graduate students also benefit from our close links with The International Research Center of Mathematics and Mechanics of Complex Systems.
During the academic year 2020/21 we plan to organize courses, that will be mandatory for students of cycle XXXVI, on the following basic themes:
The Ph.D. COLLOQUIUM
Monday June 8th 2:30 p.m. - ZOOM Videoconference platform
Prof. Philip Protter
Statistics Department, Columbia University
Nonlinear Valuation in Credit Risk
Abstract: In a series of recent papers, Damiano Brigo, Andrea Pallavicini, and co-authors have shown that the value of a contract in a Credit Valuation Adjustment (CVA) setting, being the sum of the cash flows, can be represented as a solution of a decoupled forward-backward stochastic differential equation (FBSDE).
CVA is the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counter party's default. In other words, CVA is the market value of counter party credit risk. This has achieved noteworthy importance after the 2008 financial debacle, where counter party risk played an under-modeled but huge risk.
In their analysis, Brigo et al make the classical assumption of conditional independence of the default times, given the risk-free market filtration. This does not allow for the possibility of simultaneous defaults. We weaken their assumption, replacing it with a martingale orthogonality condition. This in turn changes the form of the BSDE that arises from the model.
My talk is based on joint work with Aditi Dandapani.
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DOCTORATE COUNCIL (cycles XXXII-XXXIV)