Members
- Bruno Bouchard
- Jean-François Chassagneux
- Etienne Chevalier
- Romuald Elie (PI)
- Idris Kharroubi
- Mathieu Rosenbaum
- Vathana Ly Vath
Description
From the financial point of view, the purpose of this project is to take into consideration liquidity market frictions and risk management constraints in hedging and optimal allocation problems. From the mathematical point of view, this requires new research in statistics for random processes, theoretical mathematical finance, singular constrained stochastic control policies, highly non linear second order parabolic PDEs, regularity and discrete time approximation of Backward Stochastic Differential Equations (BSDEs). The project is divided in three main tasks, concerning respectively the design of optimal hedging policies under liquidity frictions, the characterization of optimal allocation strategies under risk constraints and finally the corresponding BSDE representation and numerical approximation.
All these problems will be discussed from the mathematical point of view in the most general possible framework and the combination of the whole program will be done on specific problems of interest in practical finance.
Publications
- Preprints
- Published papers
'Numerical simulation of quadratic BSDEs' (2013), JF Chassagneux and A. Richou, preprint.
'When terminal facelift enforces Delta constraints' (2012), JF Chassagneux, R. Elie and I. Kharroubi, preprint.
'BSDE with weak terminal condition' (2012), B. Bouchard, R. Elie & A. Reveillac.
'Approximate hedging for non linear transaction costs on the volume of traded assets' (2012), R. Elie & E. Lepinette.
'BSDE representations for optimal switching problems with controlled volatility' (2012), R. Elie & I. Kharroubi.
'Simple constructive approach to quadratic BSDEs with or without delay' (2013), Stochastic Processes and their Applications, 123(8) , Pages 2921-2939, R. Elie & P. Briand.
'Adding constraints to BSDEs with Jumps: an alternative to multidimensional reflections' (2012), Forthcoming ESAIM Probability and Statistics, R. Elie & I. Kharroubi.
'Optimal selling rules for monetary invariant criteria: tracking the maximum of a portfolio with negative drift' (2012), Forthcoming in Mathematical Finance, R. Elie & G. Espinosa.
'A note on utility based pricing and asymptotic risk diversification' (2012), Mathematics and Financial Economics, 22(3), 6-1 pp 59-74, B. Bouchard, R. Elie & L. Moreau.