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:

- Controlled Markov Processes and Viscosity Solutions, 2nd edition, (with W.H. Fleming) Springer-Verlag, (2005).

Because of copy right agreements, this link unfortunately contains only the table of contents. However, this is the link in amazon.com. - Controlled Markov Processes and Viscosity Solutions, (with W.H. Fleming) Springer-Verlag, (1993).
- Stochastic Optimal Control in Finance, Cattedra Galileiana April 2003, in Scuola Normale, Pisa.

## 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:**

**109.**Viscosity Solutions of the Eikonal Equation on the Wasserstein Space, (with Qinxin Yan), arXiv:2308.04097v2, preprint, (2023).

**108.**Deep Level-set Method for Stefan Problems, (with Mykhaylo Shkolnikov and Valentin Tissot-Daguette), arXiv:2306.11601, preprint, (2023).

**107.**Viscosity solutions of McKean-Vlasov controlon a torus, (with Qinxin Yan), arXiv:2212.110532v2, SIAM Journal on Control and Optimization, (2022), to appear.

**106.**Syncronization in a Kuramoto mean field game, (with Rene Carmona and Quentin Cormier), arXiv:2210.12912v1, Communication on Partial Differential Equations, (2022), to appear.

**105.**Neural Optimal Stopping Boundary, (with Max Reppen and Valentin Tissot-Daguette), arXiv:2205.04595, preprint, (2022).

**Articles:**

**2022:**

**104.**Deep Stochastic Optimization in Finance, (with Max Reppen and Valentin Tissot-Daguette), arXiv:2205.04604, Digital Finance, (2022).

**103.**Deep Empirical Risk Minimization in finance: looking into the future, (with Max Reppen), arXiv:2011.09349v1, Mathematical Finance, (2022).

**102.**Leveraged Exchange-Traded Funds with Market Closure and Frictions, (with Min Dai, Steven Kuo and Chen Yang), Management Science, (2022).

**2021:**

**101.**Discrete dividend payments in continuous time, (with Jussi Keppo and Max Reppen), arXiv:1805.05077v1, Mathematics of Operations Research, 46, 3, 895-911, (2021).

**100.**Viability and arbitrage under Knightian uncertainty, (with Matteo Burzoni and Frank Riedel), arXiv:1707.03335v2, Econometrica, 89, 3, 1207-1234, (2021).

**99.**Martingale Optimal Transport Duality, (with Patrick Cheridito, Matti Kiiski and David Proemel), Mathematische Annalen, 379, 3-4, 1685-1712, (2021).

**2020:**

**98.**Viscosity Solutions for controlled McKean-Vlasov jump-diffusions, (with Matteo Burzoni, Vincenzo Ignazio and Max Reppen), SIAM Journal on Control and Optimization, 58/3, 1676-1699, (2020).

**97.**Conditional Davis prices, (with Kasper Larsen and Gordan Zitkovic), Finance & Stochastics, 24/3, 565--599, (2020).

**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 (2018).

**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 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).

## Contact

**Mete Soner,**

**Norman John Sollenberger Professor**

**Office:**328 Sherrerd Hall

**Phone:**609-258-5130