Probability, Stochastic Analysis and their Applications.

The ICTI Ph.D. Program in Applied Mathematics offers a course of studies in Probability, Stochastic Analysis and their Applications.  The students attending the program will study both at Carnegie Mellon University and at the Mathematics Departments of three Portuguese institutions: Faculdade de Ciências / Universidade de Lisboa, Faculdade de Ciências e Tecnologia / Universidade Nova de Lisboa, Instituto Superior Técnico / Universidade Técnica de Lisboa.

Ph.D. graduates of the program will earn two doctoral degrees, one from Carnegie Mellon University and the other from the Portuguese partners in association, currently the Universidade Tecnica de Lisboa (UTL), the Universidade de Lisboa (UL), and the Universidade Nova de Lisboa (UNL). 

The ICTI Program in Applied Mathematics with an emphasis on Probability, Stochastic Analysis and their Applications does not offer a Ph.D. degree in Mathematical Finance or Computational Finance.

Degree Requirements.

During their studies the students are expected to fulfill the following requirements. A student should complete the Qualifying Oral Examination no later than the beginning of the third year.The student is required to write a Doctoral Thesis. It should be based on research in Probability Theory/Stochastic Analysis and display depth and originality.

It is expected that the student's academic work in the program will be organized as follows:
    1. First year: Course work at one or more of the Portuguese universities.
    2. Second year: Course work at CMU.
    3. Third year: Thesis and advanced course work at CMU.
    4. Fourth year (and fifth year if needed): Thesis preparation and completion in Portugal.

While in Portugal the student will have academic residence at one of the Universities, but will be able to take graduate courses at any of the Universities.

The student's work will be initially supervised by a CMU/Portuguese pair of Pro Tem (temporary) advisors and, upon the beginning of thesis work, by a CMU/Portuguese pair of scientific advisors. It is expected that the Portuguese scientific advisor will spend up to one semester at CMU during the third year and that the CMU scientific advisor will visit the Portuguese institution near the completion of the program.

During their studies at CMU the students will have Teaching Assistant duties during at least one semester. There will be no teaching related duties during the students' stay in Portugal.

The ICTI Program in Applied Mathematics with an emphasis on Probability, Stochastic Analysis and their Applications does not offer a Ph.D. degree in Mathematical Finance or Computational Finance.

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