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Deterministic and Stochastic Controlled Systems and Applications

Final Report Summary - CONTROLLED SYSTEMS (Deterministic and Stochastic Controlled Systems and Applications)

Presentation of the project:
- FP7 PEOPLE Marie Curie ITN
- Call: FP7-PEOPLE-2007-1-1-ITN
- Name: “Deterministic and Stochastic Controlled Systems and Applications”
- No. of the Project: 213841
- Members: 6 Universities (one of them comes from an ACP country)
1. Coordinator: “Alexandru Ioan Cuza” University of Iasi, Romania
2. Scientific and Technical Coordinator: Université de Bretagne Occidentale, Brest, France
3. Friedrich Schiller Universität, Jena, Germany
4. University of Manchester, United Kingdom
5. Université Cadi Ayyad, Marrakech, Morocco
6. Università degli Studi di Milano Bicocca, Milano, Italy.
- Duration: 48 months
- Start Date: 01/10/2008
- Close Date: 30/09/2012
- Key research: Controlled Systems, Stochastic Equations, and Financial Mathematics.

The project activity is divided into 9 Work packages (6 work packages are dedicated to the scientific research activities):
WP1: Project Management and RTD coordination
WP2: Existence of optimal control and optimality conditions
WP3: Controllability and observability of deterministic and stochastic controlled systems
WP4: Hamilton Jacobi Bellman equations in finite and infinite dimension
WP5: Control with constraints: viability for deterministic and stochastic systems
WP6: SDEs, SPDEs, controlled SDEs and SPDEs
WP7: Applications to actuarial mathematics and finance, and transport in porous media
WP8: Training and mobility
WP9: Industry network and dissemination

Description of work performed:
1. Recruitment:
Twelve full positions of 36 months and twelve co-directed positions for Early Stage Researchers (six ESR x two co-directed positions) were scheduled: the ITN network offered 18 positions and launched two campaigns of recruitment in 2008 and 2009 (in 2008, 5 full 3-years positions and 3 positions co-directed and in 2009, 7 full 3-years positions and 3 positions co-directed). In fact, nineteen Early Stage Researchers (ESR) were recruited inside the ITN network: a position had to be split into two co-directed positions due to recruitment problems. The recruitment of Experienced Researchers (six 6-month positions) was processed in the second period (01.10.2010 – 30.09.2012). Four Visiting Scientists (VS) were recruited for four scientific events.
At the end of the first period (01.10.2008 – 30.09.2010) three ITN teams had published a call for application on EURAXESS.
In the second period three ESR students changed the host university for the second part of their co-directed thesis. All scheduled Experienced Researchers (six 6-month positions) were recruited in the reporting second period. Eight Visiting Scientists were recruited in this period for five scientific events.
2. Scientific activity:
In the first reporting period, five scientific milestones were achieved in the second year of implementation:
Month 12:
Milestone 1: Optimal Control in finite dimension
Milestone 11: Systems of HJB equations
Month 24:
Milestone 5: Stochastic Differential Games
Milestone 13: Control under state constraints
Milestone 17: SDEs and Controlled SDEs
Except the Milestone 5, all milestones were considered as finished. Scientific papers were published in each milestone (MS1: 21 papers; MS 11: 2 papers, MS 13: one paper and MS 17: 10 papers). For milestone 5 an extension to Month 48 was proposed and it was accomplished in the second part. At the end of the first period, 90 papers have been published (80 papers were accepted/submitted or in progress).

In the second reporting period, nineteen scientific milestones (plus MS5) were achieved in the fourth year of implementation:
Month 36:
Milestone 3: BSDEs
Milestone 8: Stabilizability
Milestone 14: Stochastic viability in finite dimension
Milestone 16: Viability with delay
Milestone 19: Fractional calculus
Milestone 20: Singular SDEs
Milestone 21: Dirichlet SDEs
Month 42:
Milestone 2: Optimal control in infinite dimension
Milestone 12: Deterministic viability
Month 48:
Milestone 4: Controlled BSDEs
Milestone 6: Deterministic controllability
Milestone 7: Stochastic controllability
Milestone 9: HJB equations
Milestone 10: Stochastic HJB equations
Milestone 15: Stochastic viability in infinite dimension
Milestone 18: SPDEs
Milestone 22: Actuarial problems
Milestone 23: Problems in finance
Milestone 24: Transport in porous media
All milestones are considered as finished. At the end of the second period 113 papers have been published, 21 papers have been accepted, 34 papers have been submitted and 48 papers have been in progress.

Final results:
- A significant improvement of the career prospects of the fellows by the training for highly qualified specialists.
- Significant results in the research milestones, in both deterministic and stochastic control as well as its application in finance.

The main website of the project is hosted by the coordinator team, at the Alexandru Ioan Cuza University of Iasi (Romania): http://www.math.uaic.ro/~ITN_Marie_Curie/

Project Contacts:
“Alexandru Ioan Cuza” University
Faculty of Mathematics
Carol 1 Blvd., no. 11, 700506 Iasi, Romania
Phone: + 40 232 20 12 12 Fax: + 40 232 20 11 60