On the first four years of activity (1/10/2008  30/09/2012), the Initial Training Network project fulfilled its main objective, that of recruiting the planned number of PhD students. Also, according to the schedule of the project, there were organized seventeen network events: a school followed by a workshop in Jena, Manchester, Brest, Marrakech, Milano, Iasi and two training workshops in Jena, one in Brest, one in Marrakech and one in Iasi.
All the Early Stage Researchers recruited by the ITN Network undergo a local research and training programme as well as a networkwide training programme.
1. The local research and training consists of:

attending specialized courses as well nonspecialized courses (e.g. foreign languages);

weekly seminars concerning actual research problems; the seminars organized in the form of discussions with the participating researchers and talks given by the ESR;

study of specialized literature under supervision of the responsible scientist.
2. The network wide training courses:

participation to the School and the Workshop in Jena (March, 2009);

participation to the School and the Workshop in Manchester (August, 2009);

participation to the School and the Workshop in Roscoff(March, 2010);

participation to the Workshop in Jena (June, 2010);

participation to the School and the Workshop in Marrakech (December, 2010);

participation to the Workshop in Jena (March, 2011);
 participation to the School and the Workshop in Milano (June,July 2011);
 participation to the School in Brest (March 2012);
 participation to the Workshop in Marrakech (April 2012);
 participation to the School and the Workshop in Iasi (June, July 2012);
 participation to the Workshop in Iasi (September 2012).
Name of participant 
Status of the participant, origin 
Name of the talk 
Andrii ANDRUSIV 
ESR, Jena 
Ruin Probabilities for the CramerLundberg Model with Stochastic Premiums 
Matteo BEDINI 
ESR, Brest 
An InformationBased Approach to CreditRisk Modelling 
Elena ISSOGLIO 
ESR, Jena 
Multidimensional Stochastic Bridges: A Study via SDEs 
Monique JEANBLANC 
VS 
Credit Risk Modeling 
Shuai JING 
ESR, Brest 
Introduction to Gexpectation, GBrownian Motion and GBackward SDEs 
Qian LIN 
ESR, Brest 
Stochastic Differential Equations Driven by a GBrownian Motion 
Yuri KABANOV 
VS 
Introduction to the Theory of Financial Markets with Transaction Costs (series of lectures) 
Holger METZLER 
ESR, Milano 
The ItoNisio Theorem 
Youssef OUKNINE 
ITN member, Marrakech 
Fubini Stochastic Theorem for Lévy Sheet
abd Applications 
Adrian ZALINESCU 
ITN member, Iasi 
Variational Inequalities Driven by Lévy Processes 
Name of participant 
Status of the participant, origin 
Name of the talk 
Khaled BAHLALI 
ITN member, Brest 
Some BSDEs and Semilinear PDEs with
Discontinuous Coefficients. Applications to the Homogenization of PDEs 
Seid BAHLALI 
ITN member, Marrakech 
General Necessary and Sufficient
Optimality Conditions for Relaxed and Strict Control Problems 
Rainer BUCKDAHN 
Scientific Coordinator, Brest 
MeanField BSDEsProperties and Associated Nonlocal PDEs 
Boulakhras GHERBAL 
ITN member, Marrakech 
Optimality Conditions of Controlled
Backward Doubly Stochastic Differential Equations 
Monique JEANBLANC 
VS 
A Density Model for Credit Risk: What
Happens after Default? 
Yuri KABANOV 
VS

Financial Markets with Friction 
Brahim MEZERDI 
ITN member, Marrakech 
Existence and Optimality Necessary in Stochastic Control of FBSDEs 
Marc QUINCAMPOIX 
ITN member, Brest 
On Limiting Values of Stochastic Differential Equations with Small Noise Intensity Tending to Zero 
Catherine RAINER 
ITN member, Brest 
Existence of an Optimal Control for Stochastic Control Systems with Nonlinear Cost Functional 
Aurel RASCANU 
Coordinator, Iasi 
Stochastc Variational Inequalities in Noncovex Domains 
Tusheng ZHANG 
ITN member, Manchester 
Boundary Value Problems of Second Order
Elliptic Operators with Singular Coefficients 
Name of participant 
Status of the participant, origin 
Name of the talk 
Rainer BUCKDAHN 
Scientific Coordinator, Brest 
Backward stochastic differential
equations and related method in stochastic control (series of lectures) 
Ron DONEY 
ITN member, Manchester 
Fluctuation theory of Levy processes (series of lectures) 
Anouar Mohamed GASSOUS 
ESR, Iasi 
Stochastic differential equations with oblique reflection 
Elena ISSOGLIO 
ESR, Jena 
On a stochastic transport equation with fractional noise 
Bernt ØKSENDAL 
VS 
Malliavin calculus for Levy processes and applications (series of lectures) 
Marcus RIEDLE 
ITN member, Manchester 
Stochastic processes in Banach spaces (series of lectures) 
Juan YANG 
ESR, Manchester 
White noise driven SPDEs with two reflected walls 
Tusheng ZHANG 
ITN member, Manchester 
Stochastic evolution equations and stochasticpartial differential equations ( series of lectures) 
Name of participant 
Status of the participant, origin 
Name of the talk 
Viorel BARBU 
ITN member, Iasi 
The ergodicity of a phase field system perturbed by noise 
Rainer BUCKDAHN 
Scientific Coordinator, Brest 
Nonlinear stochastic differential games
involving a major player and a large number of minor players 
Ovidiu CARJA 
ITN member, Iasi 
Regularity of the state constrained minimal time function 
HansJurgen ENGELBERT 
ITN member, Brest 
On normal martingales and the structure equation: a new approach 
Teodor HAVARNEANU 
ITN member, Iasi 
On the convergence of an approximation scheme for the viscosity solution of the Bellman equation arising in a stochastic optimal control problem 
Lucian MATICIUC 
ITN member, Iasi 
BSVIs under locally bounded growth 
Bernt ØKSENDAL 
VS 
Optimal control of PDEs and forwardbackward SDEs, with applications to risk minimization 
Marc QUINCAMPOIX 
ITN member, Brest 
Stochastic optimal control and linear programming approach 
Martina ZAHLE 
ITN member, Jena 
Heat kernels, potential spaces and applications to SPDE 
Adrian ZALINESCU 
ITN member, Iasi 
Viscosity solutions for systems of parabolic variational inequalities 
Name of participant 
Status of the participant, origin 
Name of the talk 
Juan LI & Rainer BUCKDAHN 
VS and Scientific Coordinator, Brest 
2 Persons ZeroSum Stochastic Differential Games 
Marco FUHRMAN & Fausto GOZZI 
ITN members, Milan 
Hamilton Jacobi Bellman equations in infinite dimensions 
Elena ISSOGLIO 
ESR, JenaManchester 
The pathwise solution of an SPDEs with fractal noise 
Hanbing LIU 
ESR, Iasi 
Maximum principle of StateConstraint optimal control governed by NavierStokes equations in 2D 
Holger METZLER 
ESR, Milan 
Backward stochastic differential equations with infinite time horizon 
Victor POSTOLACHE 
ESR, Iasi 
Filippov Type estimates for fully non linear differential inclusions 
Name of participant 
Status of the participant, origin 
Name of the talk 
Matteo BEDINI 
ESR, BrestJena 
Brownian bridge on Stochastic Interval 
Ovidiu CARJA 
ITN member, Iasi 
On strong invariance for semi linear differential inclusions 
Mhamed EDDAHBI 
ITN member, Marrakech 
Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density 
HansJuergen ENGELBERT 
ITN member, Jena 
On stochastic exponentials 
El Hassan ESSAKY 
ITN member, Marrakech 
Existence and uniqueness of solution for multidimensional BSDE with local conditions on the coefficient 
Mohammed Anouar GASSOUS 
ESR, Iasi 
Some areas of applications of SDE (BSDE) with oblique reflection 
Theodor HAVARNEANU 
ITN member, Iasi 
A Trotter Scheme for Navier Stokes equations 
Shuai JING 
ESR, Brest 
Semilinear SPDEs driven by an fBM of Hurst parameter H in (0.1/2) 
Qian LIN 
ESR, Brest 
Representation of Gmartingales as stochastic integrals with respect to GBrownian motion 
Federica MASIERO 
ITN member, Milan 
A stochastic optimal control problem for the Heat equation on the Halfline with Dirichlet Boundarynoise and Boundarycontrol 
Tianyang NIE 
ESR, Iasi 
The viability of stochastic differential equation driven by fractional Brownian motion 
Youssef OUKNINE 
ITN member, Marrakech 
The bounded variation of the flow of stochastic differential equation 
Marc QUINCAMPOIX 
ITN member, Brest 
Boundary value problems for second order stochastic differential equations with small parameters 
Aurel RASCANU 
ITN member, Iasi 
Stochastic variational inequalities with oblique subgradents 
Markus RIEDLE 
ITN member, Manchester 
Stochastic integration for Levy processes in Banach spaces 
Paolo DI TELLA 
ESR, Milan 
Linear Stochastic Schrödinger and Master Equations 
Martina ZAHLE 
ITN member, Jena 
Semigroups and stochastic partial (pseudo) differential equations on measure spaces 
Tusheng ZHANG 
ITN member, Manchester 
Semilinear Elliptic PDEs with singular coefficients 
Ying HU 
ITN member, Brest 
Quadratic and Superquadratic BSDEs and Related PDEs 
Name of participant 
Status of the participant, origin 
Name of the talk 
Monique JEANBLANC 
VS 
Enlargement of Filtrations An Introduction (270 minutes) 
Andrii ANDRUSIV 
ESR, Brest 
Two Examples Related to Minimal entropy Martingale Measures 
Matteo BEDINI 
ESR, BrestJena 
Modelling Information for Credit Risk 
Name of participant 
Status of the participant, origin 
Name of the talk 
Elena ISSOGLIO 
ESR, JenaManchester 
On a stochastic transport equation with fractale noise 
Andrii ANDRUSIV 
ESR, Jena 
On Minimal Entropy Martingale Measures 
Aurel RASCANU 
Coordinator, Iasi 
Stochastic Variational Inequalities (series of lectures) 
Christine GRUN 
ESR, Brest 
Stochastic Differential Games with Incomplete Information 
Victor POSTOLACHE 
ESR, Iasi 
Approximate weak invariance for semilinear differential inclusions in Banach spaces 
Rainer BUCKDAHN 
Scientific Coordinator, Brest 
Regularity properties of HamiltonJacobiBellman equations. A BSDE approach (series of lectures) 
Adrian ZALINESCU 
ITN member, Iasi 
Control problems for SDEs with oblique reflection 
Soufiane AAZIZI 
ESR, Marrakech 
Portfolioconstrained Backward SDEs with Jump and Related variational inequality 
Youssef OUKNINE 
ITN member, Marrakech 
Pathwise uniqueness for SDE with jumps and local time 
M'hamed EDDAHBI 
ITN member, Marrakech 
On a class of BSDE with quadratic growth 
Mateo BEDINI 
ESR, JenaBrest 
Information process and enlargement of filtration 
Mohamed ERRAOUI 
ITN member, Marrakech 

Huyen PHAM 
VS 
Stochastic control in finance (series of lectures) 
Stephane CREPEY 
VS 
BSDE modeling of financial derivatives (series of lectures) 
Said HAMADENE 
VS 
Optimal switching and BSDEs (series of lectures) 
Monique PONTIER 
VS 
Pricing rules under asymmetric information (series of lectures) 
Andrzej ROZKOSZ 
VS 
BSDEs and PDEs in divergence form (series of lectures) 
Name of participant 
Status of the participant, origin 
Name of the talk 
Viorel BARBU 
ITN member, Iasi 
The dual HamiltonJacobi Equation associated with Stochastic Optimal Control 
Teodor HAVARENEAU 
ITN member, Iasi 
Remarks on Controlability results of Magnetobydiodynamic Equations 
Eduard Rotenstein 
ITN member, Iasi 
Convex optimization problems and BSDEs driven by maximal monotone operators 
Brahim MEZERDI 
ITN member, Marrakech 
On some aspects of singular stochastic control 
Marc QUINCAMPOIX 
ITN member, Brest 
Lipschitz Continuity and Semiconcavity Properties of the Value Function of a Stochastic Control 
Catherine RAINER 
ITN member, Brest 
Regularity properties of HamiltonJacobiBellman equations 
Holger METZLER 
ESR, Milan 
An ergodic stochastic game with n players 
Mohamed HASSANI 
ITN member, Marrakech 
General existence results for BSDE 
Tusheng ZHANG 
ITN member, Manchester 
Small Random Perturbation of a kind of FBSCS 
HansJürgen ENGELBERT 
ITN member, Jena 

El Hassan ESSAKY 
ITN member, Marrakech 
BSDE With Two Reflecting Barriers and Stochastic Quadratic Growth: Application to Dynkin Game 
Khaled BAHLALI 
ITN member, Brest 
Unicite forte pour une EDS a coefficients de croissance surlineaire 
Name of participant 
Status of the participant, origin 
Name of the talk 
Aazizi, Soufiane 
ESR, Marrakech 

Andrusiv, Andrii 
ESR, Jena 
On Minimal Entropy Martingale Measures 
Bedini, Matteo 
ESR, JenaBrest 
Information and Credit Risk 
Blei, Stefan 
ER, Brest 

Buannic, Fanny 
Project manager, Brest 

Buckdahn, Rainer 
Scientific Coordinator, Brest 

Diomande, Bakarime 
ESR, Iasi 
SDEs with delay 
Di Tella, Paolo 
ESR, Jena 

Eddahbi, Mhamed 
ITN member, Marrakech 
Chaos Expansion of some Functionals of the fBm and Levy Processes and Applications 
El Asri, Brahim 
ER, Jena 

Engelbert, HansJurgen 
ITN member, Jena 

Grun, Christine 
ESR, Brest 

Hinz, Michael 
ITN member, Jena 

Ibragimov, Anton 
ESR, Milano 
Parabolic SDE in Infinite Dimensions over Gexpectatins 
Issoglio, Elena 
ESR, JenaBrest 

Jing, Shuai 
ESR, Brest 
SPDE driven by a Fractional Brownian Motion of Hurst Coeffcient 1/2<H<1. Study through its Doubly Stochastic Interpretation 
Lin, Qian 
ESR, Brest 
Nash Equilibria for 2Persons NonZero Sum Stochastic Differential Games in a general Setting 
Maticiuc, Lucian 
ITN member, Iasi 
Multivalued Backward Stochastic Differential Equations driven by Fractional Brownian Motion with Hurst Parameter H > 1/2 
Metzler, Holger 
ESR, Milano 

Quincampoix, Marc 
ITN member, Brest 

Rainer, Catherine 
ITN member, Brest 
Holder Regularity for Viscosity Solutions of fully Nonlinear HamiltonJacobi Equations with SuperQuadratic Growth in the Gradient 
Rascanu, Aurel 
Coordinator, Iasi 

Rotenstein, Eduard Paul 
ITN member & Project manager, Iasi 

Yang, Juan 
ESR, Iasi 
Existence and Uniqueness of Invariant Measure of SPDE with Reflection 
Zahle, Martina 
ITN member, Jena 

