Publications

The current publication list can be found in the MathSciNet of the American Mathematical Society, or in web of science, or in Google Scholar.

Books:

Lecture Notes and Chapters in Books:

  • Optimal control of jump-markov processes and viscosity solutions, Institute for Mathematics and Its Applications, Vol. 10, p. 501, (1986).
  • The problem of super-replication under constraints, (with N. Touzi) in Paris-Princeton Lectures on Mathematical Finance editors R.A. Carmona, E. Cinlar, I. Ekeland, E. Jouini, J. Scheinkman, N. Touzi, Lecture Notes in Mathematics 1814, Springer-Verlag, (2002).
  • Variational and Dynamic Problems for the Ginzburg-Landau Functional, in Mathematical Aspects of Evolving Interfaces, editors P. Colli and J.F. Rodrigues, Lecture Notes in Mathematics 1812, Springer-Verlag, (2000).
  • Dynamic Programming and Viscosity Solutions, Lectures in the Annual AMS 1999 Meeting in San Antonio, TX, (1999).
  • Convergence of the phase-field equations to the Mullins-Sekerka problem with kinetic undercooling, in Fundamental contributions to the continuum theory of evolving phase interfaces in solids, 413–471, Springer, Berlin, (1999).
  • Front Propagation, in Boundaries, interfaces, and transitions (Banff, AB, 1995) CRM Proc. Lecture Notes 13, AMS, 185–206, (1998).
  • Controlled Markov Processes, Viscosity Solutions and Applications to Mathematical Finance, in Viscosity Solutions and Applications, editors I. Capuzzo Dolcetta and P.L. Lions, Lecture Notes in Mathematics 1660, Springer-Verlag, (1997).
  • Flow by mean curvature of surfaces of any codimension, (with L. Ambrosio), in Variational methods for discontinuous structures, (Como, 1994), Progr. Nonlinear Differential Equations Appl., 25, Birkhäuser, Basel, 123–134, (1996).
  • 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).

Preprints:


101. Viscosity Solutions for controlled McKean-Vlasov jump-diffusions, (with Matteo Burzoni, Vincenzo Ignazio and 335v2, SIAM Journal on Control and Optimization, 58/3, 1676-1699, (2020).
100. Viability and arbitrage under Knightian uncertainty, (with Matteo Burzoni and Frank Riedel), arXiv:1707.03335v2, (2017).
99. Discrete dividend payments in continuous time, (with Jussi Keppo and Max Reppen), arXiv:1805.05077v1, Mathematics of Operations Research (forthcoming), (2018).

Articles:

2020:

98. Martingale Optimal Transport Duality, (with Patrick Cheridito, Matti Kiiski and David Proemel), Mathematische Annalen (forthcoming), (2019).
97. Conditional Davis prices, (with Kasper Larsen and Gordan Zitkovic), Finance & Stochastics (forthcoming), (2017).
96.Dividends with random profitability rate, (with Max Reppen and Jean-Charles Rochet), Mathematical Finance, 30/1, 228-259, (2020).

2019:

95. Second order stochastic target problems with generalized market impact, (with Bruno Bouchard, Gregoire Loeper and Chao Zhou), SIAM Journal on Control and Optimization, 57 (6), 4125-4149, (2019).

2018:

94. Constrained optimal transport, (with Ibrahim Ekren), arXiv:1610.02940v1, Archive for Rational Mechanics, 227/3, 929-965 (2017). 

2017:

93. A primer on portfolio choice with small transaction costs, (with Johannes Muhle-Karbe and Max Reppen), arXiv:1612.01302v1, Annual Review of Financial Economics, 9, 301-331 (2017).
92. Optimal consumption and investment with fixed and proportional transaction costs, (with Albert Altarovici and Max Reppen), arXiv:1610.03958, SIAM J. Control and Optimization, 55,1673–1710, (2017).
91. Convex duality with transaction costs, (with Yan Dolinsky), arXiv:1502.01735, Mathematics of Operations Research, 42/2,448–471, (2017).
90. Trading with small impact, (with L. Moreau and J. Muhle-Karbe), arXiv:1402.5304, Mathematical Finance, 27/2,350–400, (2017).
89. Hedging with temporary price impact, (with Peter Bank and Moritz Voss), arXiv:1510.03223v1, Mathematics and Financial Economics, 11, 215–229,(2017).

2016:

88. Utility maximization in an illiquid market in continuous time, (with M. Vukelja), Mathematical Methods in Operations Research, 84/2, 285–321,(2016).
87. Hedging under an expected loss constraint with small transaction costs, (with B. Bouchard and L. Moreau), arXiv:1309.4916, SIAM Journal on Math. Fin., 7/1, 508–551,(2016).
86. Facelifting in utility maximization, (with K. Larsen and G. Zitkovic), arXiv:1404.2227, Finance and Stochastics, 20/1, 99–121, (2016).

2015:

85. Martingale optimal transport in the Skorokhod space, (with Y. Dolinsky), Stochastic Processes and Applications, 125/10, 3893–3931, (2015).
Erratum: Corrigendum to "Martingale optimal transport in the Skorokhod space" (with Yan Dolinsky), Stochastic Processes and Applications, (2016).
84.Asymptotics with fixed transaction costs, (with A. Altarovici and J. Muhle-Karbe), Finance and Stochastics, 19 (2), 363–414, (2015).
83. Homogenization and asymptotics for small transaction costs - the multi-dimensional case, (with D. Possamaï and N. Touzi), Communications in PDEs, (2015).

2014:

82. Robust hedging with proportional transaction costs, (with Y. Dolinsky), Finance and Stochastics, 18 (2), 327–347, (2014).
81. Approximating stochastic volatility by recombinant trees, (with E. Akyildirim and Y. Dolinsky), Annals of Applied Probability, 24/5, 2176–2205, (2014).
80. Optimal dividend policy with random interest rates, (with E. Akyildirim, I.E. Guney and J.C. Rochet), Journal of Mathematical Economics, 51, 93–101, (2014).
79. Martingale optimal transport and robust hedging in continuous time, (with Y. Dolinsky), Probability Theory and Related Fields, 160 (1–2), 391–427, (2014).
78. Hedging in an Illiquid Binomial Market, (with S. Gökay), Nonlinear Analysis. Real World Applications, 16, 1–16, (2014). 

2013:

77. Homogenization and asymptotics for small transaction costs, (with N. Touzi), SIAM Journal on Control and Optimization, 51/4, 2893–2921, (2013).
76. Resilient price impact of trading and the cost of illiquidity, (with A.F. Roch), International Journal on Theoretical and Applied Finance, 16/6, (2013).
75. Utility maximization in an illiquid market, (with M. Vukelja), Stochastics - special issue in memory of M. Taksar, 85/4, 692–706, (2013).
74. Dual Formulation of Second Order Target Problems, (with N. Touzi and J. Zhang), Annals of Applied Probability, 23/1, 308–347, (2013).
73. Vortex density models for superconductivity and superfluidity, (with S. Baldo, R.L. Jerrard, G. Orlandi), Communications in Mathematical Physics, 318/1, 131–171, (2013).
72. Duality and Convergence for Binomial Markets with Friction, (with Y. Dolinsky), Finance and Stochastics, 17 (3), 447–475, (2013).

2012:

71. Convergence of Ginzburg-Landau functionals in 3-d superconductivity, (with S. Baldo, R.L. Jerrard, G. Orlandi), Archive for Rational Mechanics and Analysis, 205/3, 699–752, (2012).
70. Liquidity in a Binomial market, (with S. Gökay), Mathematical Finance, 22/2, 250–276, (2012).
69. Large liquidity expansion for super-hedging costs, (with D. Possamaï and N. Touzi), Asymptotic Analysis, 79, Issue: 1-2, 45–64, (2012).
68. Superhedging and Dynamic Risk Measures under Volatility Uncertainty, (with M. Nutz), SIAM Journal on Control and Optimization, 50/4, 2065–2089, (2012).
67. Wellposedness of Second Order Backward SDEs, (with N. Touzi and J. Zhang), Probability Theory and Related Fields, 153, 149–190, (2012).
66. Weak Approximation of G-Expectations, (with Y. Dolinsky and M. Nutz), Stochastic Processes and their Applications, 122 (2), 664–675, (2012).

2011:

65. Martingale Representation Theorem for the G-expectation, (with N. Touzi and J. Zhang), Stochastic Processes and their Applications, 121 (2), 265–287, (2011).
64. Quasi-sure stochastic analysis through aggregation, (with N. Touzi and J. Zhang), Electronic Journal of Probability, (Article Number: 67), 16, 1844–1879, (2011).

2010:

63. Option hedging for small investors under liquidity costs, (with U. Çetin and N. Touzi), Finance and Stochastics, 14 (3), 317–341, (2010).
62. Optimal investment strategies with a reallocation constraint, (with F. Egriboyun), Mathematical Methods of Operations Research, 71(3), 551–585, (2010).
61. Merton problem with taxes: characterization, computation and approximation, (with I. Ben-Tahar and N. Touzi), SIAM Journal on Financial Mathematics, 1, 366–395, (2010).

2009:

60. 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).

2007:

59. Stochastic representations for nonlinear parabolic PDEs, survey article, (2007).
58. The dynamic programming equation for the problem of optimal investment under capital gains taxes, (with I. Ben-Tahar and N. Touzi), SIAM Journal on Control and Optimization, 48(5), 1779–1801, (2007).
57. Second order backward stochastic differential equations and fully non-linear parabolic PDEs, (with P. Cheridito, N. Touzi, and N. Victoir), Comm. on Pure and Applied Math., 60 (7): 1081–1110 (2007).
56. Hedging under Gamma constraints by optimal stopping and face-lifting, (with N. Touzi), Mathematical Finance, 17 (1): 59–79 (2007).

2005

55. Small time path behavior of double stochastic integrals and applications to stochastic control, (with P. Cheridito and N. Touzi), Annals of Applied Probability, 15/4, 2472–2495, (2005).
54. The multi-dimensional super-replication problem under gamma constraints, (with P. Cheridito and N. Touzi), Annales de l'Institute Henri Poincare Analyse Nonlineaire, 22 (5): 633–666 (2005).

2004

53. Stochastic Control for a Class of Random Evolution Models, (with M.-O. Hongler and L. Streit), Applied Mathematics and Optimization, 49: 113–121 (2004).

2003

52. A stochastic representation for mean curvature type flows, (with N. Touzi), Annals of Probability, 31/3, 1145–1165, (2003).

2002

51. Limiting behavior of the Ginzburg-Landau energy, (with R.L. Jerrard), J. Functional Analysis, 192, 524–561, (2002).
50. A stochastic representation for level set equations, (with N. Touzi), Communications in PDEs, 27(9&10), 2031–2053, (2002).
49. Dynamic programming for stochastic target problems and geometric flows, (with N. Touzi), Journal of European Mathematical Society, 4/3, 201–236, (2002).
48. The Jacobian and the Ginzburg-Landau energy, (with R.L. Jerrard), Calculus of Variations, 14, 151–191, (2002).
47. Stochastic target problems and dynamic programming, (with N. Touzi), SIAM Journal on Control and Optimization, 41, 404–424, (2002).
46. Function of higher bounded variations, (with R.L. Jerrard), Indiana University Mathematics Journal, 51/3, 645–677, (2002).

2000

45. Super-replication under Gamma constraints, (with N. Touzi), SIAM Journal on Control and Optimization, 39(1), 73–96, (2000).

1999

44. Rectifiability of the distributional Jacobian for a class of functions, (with R.L. Jerrard), C.R. Acad. Sci. Paris, t. 329, Serie I, 983–688, (1999).
43. Scaling limits and regularity for a class of Ginzburg-Landau systems, (with R.L. Jerrard), Annales L'Institute Henry Poincare, 16/4, 423–466, (1999).

1998

42. Backward SDEs with constraints on the gains process, (with J. Cvitanic and I. Karatzas), Annals of Probability, 26, 1522–1551, (1998).
41. Dynamics of Ginzburg-Landau vortices, (with R.L. Jerrard), Arc. Rat. Mech. An., 142, 185–206, (1998).
40. Regularity and convergence of crystalline motion, (with K. Ishii), SIAM Math. Analysis, 30, 19–37, (1998).
39. Optimal replication of contingent claims under portfolio constraints, (with M. Broadie and J. Cvitanic), Review of Financial Studies, 11, 59–79, (1998).
38. Option pricing with transaction costs and a nonlinear Black-Scholes equation, (with G. Barles), Finance and Stochastics, 2, 369–397, (1998).

1997

37. A measure theoretic approach to higher co-dimension mean curvature flow, (with L. Ambrosio), dedicated to Ennion de Giorgi, Ann. Scuola Normale, 25, 27–49, (1997).
36. Ginzburg-Landau equation and motion by mean curvature, I: convergence, Journal of Geometric Analysis, 7, 437–475, (1997).
35. Ginzburg-Landau equation and motion by mean curvature, II: development of the interface, Journal of Geometric Analysis, 7, 476–491, (1997).
34. Hedging in incomplete markets with HARA utility (with D. Duffie, W. Fleming, and T. Zariphopoulou), J. Economic Dynamics and Control, 21, 753–782, (1997).

1996

33. Level set approach to mean curvature flow in arbitrary codimension, (with L. Ambrosio), Journal of Differential Geometry, 43, 693–737, (1996).
32. Three-phase boundary motions under constant velocities. I: The vanishing surface tension limit, (with F. Reitich), Proc. Royal Soc. Edinburgh, 126A, 837–865, (1996).
31. Heavy traffic convergence of a controlled, multi-class, queuing system, (with L.F. Martins and S.E. Shreve), SIAM J. Cont. Opt., 34/6, 2133–2171, (1996).

1995

30. Convergence of the phase field equations to the Mullins-Sekerka problem with a kinetic undercooling, Arc. Rat. Mech. An., 131, 139–197, (1995).
29. There is no nontrivial hedging portfolio for option pricing with transaction costs, (with S.E. Shreve and J. Cvitanic), Annals of Applied Prob., 5/2, 327–355, (1995).
28. Anisotropic planar motion of an interface relaxed by the formation of infinitesimal wrinkles, (with M. Gurtin and P.E. Souganidis), J. Differential Equations, 119/1, 54–108, (1995).

1994

27. Optimal investment and consumption with transaction costs, (with S.E. Shreve), Annals of Applied Probability, 14/3, 609–693, (1994).

1993

26. Motion of a set by the curvature of its boundary, J. Differential Equations, 101, 313–372, (1993).
25. On the propagation of singularities of semi-convex functions, (with L. Ambrosio and P. Cannarsa), An. Scuola Normali Pisa, Serie IV, Vol. XX, 597–616, (1993).
24. A dynamic programming approach to nonlinear boundary control problems of parabolic type, (with P. Cannarsa and F. Gozzi), J. Functional Analysis, 117/1, 25–61, (1993).
23. Front propagation and phase field theory, (with G. Barles and P.E. Souganidis), SIAM J. Cont. Opt., 2/31, special issue dedicated to W. Fleming, 439–469, (1993).
22. Singular perturbations in manufacturing, SIAM J. Cont. Opt., 31, 132–146, (1993).
21. Uniqueness and singularities of rotationally symmetric surfaces moving by mean curvature, (with P.E. Souganidis), Comm. in PDE, 18, 859–894, (1993).

1992

20. Phase transitions and generalized motion by mean curvature, (with L.C. Evans and P.E. Souganidis), Comm. in Pure and Applied Math., 65, 1097–1123, (1992).
19. Turnpike Sets and Their Analysis in Stochastic Production Planning Problems, (with S.P. Sethi, 
Q. Zhang, and J. Jiang), Mathematics of Operations Research, 17, 4, 932–950, (1992).
18. Some remarks on the Stefan problem with surface structure, (with M.E. Gurtin), Quarterly of Applied Math., 50, 291–303 (1992).

1991

17. Optimal investment and consumption with two bonds and transaction costs, (with S.E. Shreve and G.-L. Xin), Mathematical Finance, 1/3, 53–84, (1991).
16. A boundary value problem for Hamilton-Jacobi equations in Hilbert spaces, (with P. Cannarsa and F. Gozzi), Applied Mathematics and Optimization, 24, 197–220, (1991).
15. A free boundary problem related to singular stochastic control: parabolic case, (with S.E. Shreve), Comm. PDE, 16, 373–424, (1991).
14. An asymptotic analysis of hierarchical control of manufacturing systems, (with J. Lehoczky, S. Sethi, and M. Taksar), Math. O.R., 16/3, 596–608, (1991).

1990

13. A viscosity solution approach to the asymptotic analysis of queueing systems, (with P. Dupuis and H. Ishii), Annals of Probability, 18/1, 226–255, (1990).

1989

12. Asymptotic expansions for Markov processes with Levy generators, (with W. Fleming), Applied Mathematics Optimization, 19, 203–223, (1989).
11. Generalized one-sided estimates for solutions of Hamilton-Jacobi equations and applications, (with P. Cannarsa), Nonlinear Analysis, Theory, Methods, 13/3, 305–323, (1989).
10. Regularity of the value function of a two-dimensional singular stochastic control problem, (with S.E. Shreve), SIAM J. Cont. Opt., 27/4, 876–907, (1989).

1988

9. Mixing Markov chains and their images, (with M. Barnsley and M. Berger), Probability in Eng. and Inf. Sci., 387–414, (1988).
8. Random walks generated by affine mappings, (with M. Berger), J. Theoretical Probability, 1/3, 239–254, (1988).
7. On the Hamilton-Jacobi equations in Banach spaces, J.O.T.A., 57/3, 429–437, (1988).

1987

6. A remark on the large deviations of an ergodic Markov process, (with W. Fleming and S.-J. Sheu), Stochastics, 22, 187–199, (1987).
5. An optimal stochastic production planning problem with randomly fluctuating demand, (with W. Fleming and S. Sethi), SIAM J. Cont. Opt., 25, 1494–1502, (1987).
4. On the singularities of the viscosity solutions to Hamilton-Jacobi equations, (with P. Cannarsa), Indiana University Mathematics Journal, 36/3, 501–524, (1987).

1986

3. Optimal Control with state-space constraint II, SIAM J. Cont. Opt., 24/3, 1110–1122, (1986).
2. Optimal Control with state-space constraint I, SIAM J. Cont. Opt., 24/3, 552–562, (1986).

1985

1. Optimal control of a one-dimensional storage process, Appl. Math. Opt., 13, 175–191, (1985).

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