Mathematical Methods for Robust Financial Risk Management


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 Nazionalità Coordinatore France [FR]
 Totale costo 1˙871˙400 €
 EC contributo 1˙871˙400 €
 Programma 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)
 Code Call ERC-2012-ADG_20120216
 Funding Scheme ERC-AG
 Anno di inizio 2013
 Periodo (anno-mese-giorno) 2013-05-01   -   2018-04-30


# participant  country  role  EC contrib. [€] 

 Organization address address: ROUTE DE SACLAY
postcode: 91128

contact info
Titolo: Mrs.
Nome: Laurence
Cognome: Roulet
Email: send email
Telefono: 33169333254
Fax: 33169333289

FR (PALAISEAU) hostInstitution 1˙871˙400.00

 Organization address address: ROUTE DE SACLAY
postcode: 91128

contact info
Titolo: Prof.
Nome: Nizar
Cognome: Touzi
Email: send email
Telefono: +33 1 69 33 46 23
Fax: +33 1 69 33 46 46

FR (PALAISEAU) hostInstitution 1˙871˙400.00


 Word cloud

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numerical    probabilistic    intend    direction    problem    techniques    financial    mathematics    equations    questions    connection    theory    corresponding    equation    markets    mean    risk   

 Obiettivo del progetto (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.'

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