Objective Reliable techniques in finance should take into account the unavoidable modelling error. This is the main focus of this project that we intend to address from two viewpoints raising new questions in applied mathematics.Our first research direction is to device robust risk management methods which use the market observations and the no-arbitrage principle. A classical result in financial mathematics essentially states that, in idealized frictionless financial markets, the price processes of tradable securities must be a martingale under some equivalent probability measure. We propose to adopt a conservative viewpoint by deriving the bounds over all possible choices of martingales. By accounting for the rich information corresponding to the prices of European call options, we arrive naturally to a new optimal transportation problem. We intend to analyze several questions: clarify the connection with the Skorohod embedding problem, understand better the duality, develop the corresponding numerical techniques, explore the robust portfolio optimization problems under such constraints, and understand their impact on the risk measurement.The second direction of research proposed in this project concerns the recent theory of Mean Field Games, recently introduced by Lasry and Lions. Our intention is to address this theory from the probabilistic point of view. The main observation is that the MFG equations, consisting of a coupled system of a Fokker-Planck equation and a semilinear Hamilton-Jacobi-Bellman equation, can be viewed as an extension of the theory of forward-backward stochastic differential equations (FBSDE) with mean-field dependence. This theory provides a simple modelling of the interactions which may be used to explain important phenomena on financial markets as the contagion effect and the systemic risk. In particular, the connection with FBSDEs opens the door to probabilistic numerical methods. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisdifferential equations Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2012-ADG_20120216 See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution ECOLE POLYTECHNIQUE EU contribution € 1 871 400,00 Address ROUTE DE SACLAY 91128 Palaiseau Cedex France See on map Region Ile-de-France Ile-de-France Essonne Activity type Higher or Secondary Education Establishments Administrative Contact Denis Guilbaud (Mr.) Principal investigator Nizar Touzi (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all ECOLE POLYTECHNIQUE France EU contribution € 1 871 400,00 Address ROUTE DE SACLAY 91128 Palaiseau Cedex See on map Region Ile-de-France Ile-de-France Essonne Activity type Higher or Secondary Education Establishments Administrative Contact Denis Guilbaud (Mr.) Principal investigator Nizar Touzi (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
