In 2008, Soner was awarded an Advanced Research grant by the European Research Council. The project, entitled Mathematical Methods for Financial Risk Management (abbreviated FiRM), aims to develop new tools to analyze problems in which control problems or risk measures are defined through probability measures that are orthogonal to each other. Since its initiation in December 2008 in Istanbul, one major research workshop

Istanbul Workshop on Mathematical Finance

has been organized in Istanbul in May 2009. Many short term research visits have been supported by this grant as well. In addition, the following researchers have received long term support from this grant and the following research articles have resulted.

Researchers Supported by FiRM

Postdoctoral Fellows

• Prof. Alexandre Roch (September 2009-July 2010), ESG UQAM, Montreal, Canada
• Dr. Idris Kharroubi (January 2010-June 2010), Ceremade, University of Paris IX, Dauphine, France
• Dr. Gilles-Edouard Espinosa (September 2010-February 2011), ENPC (Cermics), Paris, France
• Prof. Yan Dolinsky (February 2010-September 2012), Department of Statistics, Hebrew University, Jerusalem, Israel
• Prof. Marcel Nutz (October 2010-September 2011), Department of Mathematics, Columbia University, New York, USA
• Dr. Marcus Wunsch (May 2011 - current)
• Dr. Anja Richter (September 2011 - current)
• Dr. Ludovic Moreau (October 2012 - current)
• Dr. Dylan Possamaï (March 2013), CMAP, Ecole Polytechnique, Paris, France

Graduate Students

• Mr. Erdinç Akyildirim
• Mr. Albert Altarovici
• Dr. Selim Gökay (graduated in 2011)
• Mr. Mario Sikic
• Ms. Mirjana Vukelja

Publications

preprints:

• 25. Asymptotics with fixed transaction costs, (with A. Altarovici and J. Muhle-Karbe), submitted to Finance and Stochastics, (2013), forthcoming.
  24. Approximating stochastic volatility by recombinant trees, (with E. Akyildirim and Y. Dolinsky), submitted to Annals of Applied Probability, (2013), forthcoming.
  23. Robust hedging with proportional transaction costs, (with Y. Dolinsky), Finance and Stochastics, (2013), forthcoming.
  22. Homogenization and asymptotics for small transaction costs - the multi-dimensional case, (with
  D. Possamaï and N. Touzi), submitted to Communications in PDEs, (2013), preprint.
  21. Optimal dividend policy with random interest rates, (with E. Akyildirim, I.E. Guney and J.C. Rochet), (2012), preprint.
  20. Martingale optimal transport and robust hedging in continuous time, (with Y. Dolinsky), submitted to Probability Theory and Related Fields, (2013), forthcoming.
  
  2013:
  
  19. Hedging in an Illiquid Binomial Market, (with S. Gökay), Nonlinear Analysis. Real World Applications, 16, 1–16, (2014).
  18. Homogenization and asymptotics for small transaction costs, (with N. Touzi), SIAM Journal on Control and Optimization, 51/4, 2893–2921, (2013).
  17. Resilient price impact of trading and the cost of illiquidity, (with A.F. Roch), International Journal on Theoretical and Applied Finance, 16/6, (2013).
  16. Utility maximization in an illiquid market, (with M. Vukelja), Stochastics - special issue in memory of M. Taksar, 85/4, 692–706, (2013).
  15. Optimal selling rules for monetary invariant criteria: tracking the maximum of a portfolio with negative drift, (by R. Elie and G.-E. Espinosa), Mathematical Finance, (2013), forthcoming.
  14. Dual Formulation of Second Order Target Problems, (with N. Touzi and J. Zhang), Annals of Applied Probability, 23/1, 308–347, (2013).
  13. Duality and Convergence for Binomial Markets with Friction, (with Y. Dolinsky), Finance and Stochastics, 17 (3), 447–475, (2013).
  
  2012:
  
  12. Liquidity in a Binomial market, (with S. Gökay), Mathematical Finance, 22/2, 250–276, (2012).
  11. Large liquidity expansion for super-hedging costs, (with D. Possamaï and N. Touzi), Asymptotic Analysis, 79, Issue: 1-2, 45–64, (2012).
  10. Superhedging and Dynamic Risk Measures under Volatility Uncertainty, (with M. Nutz), SIAM Journal on Control and Optimization, 50/4, 2065–2089, (2012).
  9. Wellposedness of Second Order Backward SDEs, (with N. Touzi and J. Zhang), Probability Theory and Related Fields, 153, 149–190, (2012).
  8. Weak Approximation of G-Expectations, (with Y. Dolinsky and M. Nutz), Stochastic Processes and their Applications, 122 (2), 664–675, (2012).
  
  2011:
  
  7. Liquidity Models in Continuous and Discrete Time, (with S. Gökay and A.F. Roch), in Advanced Mathematical Methods for Finance, editors G. Di Nunno and B. Øksendal, Springer-Verlag, 333–366, (2011).
  6. Martingale Representation Theorem for the G-expectation, (with N. Touzi and J. Zhang), Stochastic Processes and their Applications, 121 (2), 265–287, (2011).
  5. Quasi-sure stochastic analysis through aggregation, (with N. Touzi and J. Zhang), Electronic Journal of Probability, (Article Number: 67), 16, 1844–1879, (2011).
  4. A note on existence and uniqueness to Multidimensional reflected BSDEs, (by J.-F. Chassagneux,
  I. Kharroubi and R. Elie), Electronic Communications in Probability, 16, 120–128, (2011).
  
  2010:
  
  3. Optimal Portfolio Liquidation with Execution Cost and Risk, (by I. Kharroubi and H. Pham), SIAM J. Finan. Math., Volume 1, 897–931 (2010).
  2. Option hedging for small investors under liquidity costs, (with U. Çetin and N. Touzi), Finance and Stochastics, 14 (3), 317–341, (2010).
  
  2009:
  
  1. The dynamic programming equation for second order stochastic target problems, (with N. Touzi), SIAM Journal on Control and Optimization, Vol. 48, No. 4, 2344–2365, (2009).