René Carmona

Paul Wythes ’55 Professor of Engineering and Finance


  1. Laplaciens sur un espace de Wiener abstrait, C.R. Acad. Sci. Paris ser. A 278 (1974) 933-936.

  2. Module de continuite uniforme des mouvements browniens a valeurs dans un espace de Banach, C.R. Acad. Sci. Paris ser. A 281 (1975) 659-662.

  3. (with N. Kono), Convergence en loi et lois du lagarithme itere pour les vectures gaussiens, Z. Wahrscheinlichkeitstheorie verw. Gebiete 36 (1976) 241-267.

  4. Lois du logarithme itere pour les suites de vecteurs gaussiens, Ann. Sci. Univ. Clermont 61 (1976) 5-9.

  5. Measurable Norms and some Banach Space Valued Gaussian Processes, Duke Math Journal 44 (1977) 109-127.

  6. Potentials on Abstract Wiener Spaces, J. of Functional Analysis 26 (1977) 215-231.

  7. Tensor Products of Gaussian Measures, Proceedings of Conference of Vector Space Measures and Applications, Dublin 1977, Lect. Notes in Math

  8. Pointwise Bounds for Schroedinger Eigenstates, Comm. Math. Phys. 62 (1978) 97-106.

  9. (with S. Chevet) Tensor Gaussian Measures on Lv(E), J. of Functional Analysis 33 (1979) 251-296.

  10. Regularity Properties of Schroedinger and Dirichlet Semigroups, J. of Functional Analysis 33 (1979) 251-296.

  11. Banach Space Valued Gaussian Precesses, Proceedings of Conference on Probability on Banch Space II, Obverwolfach (June 1978), Lect. Notes in Math.,

  12. Operateurs doe Schroedinger a resolvante compacte, Sem. Proba. XIII, Lect. Notes in Math.,

  13. Processus de diffusion gouverne par la forme de Dirichlet de l'operateur de Schroedinger, Sem. Proba. XIII, Lect. Notes in Math.,

  14. Etude Probabiliste de l'Operateur de Schroedinger, Ann. Sci. Univ. Clermont. (1979)

  15. Infinite Dimensional Newtonian Potentials, Proceedings of Conference on Probability Theory on Vector Spaces II, Wroclaw (Poland), (September 1979), Lect. Notes in Math.,

  16. (with Barry Simon) Pointwise Bounds on Eigenfunctions and Wave Packets in N Body Quantum systems V. Lower Bounds and Path Integrals, Comm. in Math. Phys. 80 (1981), 59-98.

  17. Trajectoires du Processus de Mouvement Brownien et Operateur de Schroedinger, Actes du Collogue International du C.N.R.S., June 1980, Saint Flour, Publications du C.N.R.S. (1981).

  18. Exponential Localization for One Dimensional Schroedinger Equation with a Random Potential, Duke Math Journal 49 (1982), 191-213.

  19. (with A. Klein) Exponential Moments for Hitting Times of Uniformly Ergodic Markov Processes, Ann. Proba. 11 (1983), 648-655.

  20. (with J. Berruyer) Convergence vague et decomposition de Riesz dans des groupes non localement compacts, Sem. Theo. Potentiel no.6, Lect. Notes in Math.,

  21. (with F. Bentosela et. al.) Schroedinger operators withan electric field and random or deterministic potential, Comm. Math. Phys. 88 (1983), 387-397.

  22. Spectral Properties of one dimensional Schroedinger Operators with Deterministic and Random Potentials: New Spectral Types, J. of Functional Analysis 51 (1983), 229-258.

  23. Absolute Continuous Spectrum of One-Dimensional Schroedinger Operators, in Differential Equations, e.d. I. W. Knowles and R. T. Lewis, North Holland (1984).

  24. One Dimensional Schrodinger Operators with Random Potentials. Physics 124A (1984) 181-188.

  25. One Dimensional Schrodinger Operators: A Survey, Acta Applicandae Mathematicae, 4 (1985) 65-91.

  26. (with A. Antoniadis) Infinite Dimensional Ornstein Ulhenbeck Processes, Probab. Th. Rel. Fields74, 31-54.

  27. Probabilistic Construction of Nelson's Processes, in Proceedings of the Taniguchi Symp. on Stochastic Processes & Random Media. (1985) North Holland (1987).

  28. (with J. Brossard) Can you hear the dimensional of a fractal? Comm. Math. Phys. 104 (1986) 103-122.

  29. Exercises for a book of random potentials, in Proceedings of the IMA vol

  30. (with A. Klein and F. Martinelli) Anderson Localization for Bernoulli and other Singular Potentials. Comm. Math. Phys. 108 (1987) 41-66.

  31. (with D. Nualart) Random non-linear wave equations: propagation of singularities. Ann. Proba. 16 (1988) 730-751.

  32. (with D. Nualart) Random non-linear wave equations: existence and regularity properties of the solutions. Proba. Theory and Relat. Fields 79 (1988) 469-508.

  33. (with S. Kotani) Inverse spectral theory for random Jacobi matrices. J. Stat. Physics. 46 (1987) 1091-1114.

  34. Path Integrals for Relativistic Schr"odinger Operators. in Schrodinger Operators, H.Holden & A. Jensen (Eds). Lect. Notes in Phys.

  35. (with W. Chen-Masters and B. Simon) Relativistic Schrodinger Operators: Asymptotic Behavior of the Eigenfunctions. J. Functional Analysis, 91 (1990) 117-142.

  36. (with D. Nualart) Traces of Random Variables on Wiener Space and the Onsager-Machlup Functional. J. Functional Anal. 107, (1992) 402-438.

  37. (with W. Zheng) Reflected Brownian Motions and Comparison Theorems for Neumann Heat Kernels. J. Functional Anal. 123, 109-128.

  38. (with S.A. Molchanov) Intermittency and Phase Transitions for some Particle Systems in Random Media. in Asymptotic problems in probability theory: stochastic models and diffusions on fractals. K.D. Elworthy & N. Ikeda Eds. (1993), 15-36.

  39. (with H.S. Ahn and S.A. Molchanov) Parabolic Anderson Problem with Levy Potentials. Lect. Notes in Control and Info. Sci.

  40. (with J.P. Fouque) Diffusion Approximation for Two Parameter Processes. Probab. Theory Relat. Fields 98, (1994) 277-298.

  41. Wavelet Detection of Transients in Noisy Time Series. (preprint).

  42. (with A. Antoniadis and J. Berruyer): Learning Data Analysis and Mathematical Statistics with a Macintosh, in Statistics and Computing eds W. Haerdle & L. Simar, Computer Intensive Methods in Statistics, Physica Verlag (1993), 73-85.

  43. Spline Smoothing & Extrema Representation: Variations on a Reconstruction Algorithm of Mallat and Zhong. in Wavelets and Statistics, eds A. Antoniadis & G. Oppenheim}, Lect. Notes in Statist. 103, 83-94.

  44. Wavelet Identification of Transients in Noisy Signals. Proc. SPIE Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1993) 392-400.

  45. (with S.A. Molchanov): Stationary Parabolic Anderson Model and Intermittency Probab. Theory and Related Fields, 102 433-453.

  46. (with D. Nualart) Gradient Estimates and Parabolic Equations with Random Boundary Conditions. (preprint)

  47. (with J.P. Fouque) Diffusion Approximation for the Advection Diffusion of a Passive Scalar in a Gaussian Space Time Velocity Field. in Progress in Probab. Vol. 36 pp. 37-49, Birkha"user, N.Y.

  48. (with J.A. Yan) A New Space f White Noise Distributions and Applications to SPDE's in Progress in Probab. Vol. 36 pp. 51-66, Birkha"user, N.Y.

  49. (with W. Hwang and R.D. Frostig): Wavelet Analysis for Brain Function Imaging. IEEE Trans. on Medical Imaging 14 (1995) 556-564.

  50. (with W.L. Hwang and B. Torresani): Characterization of Signals by the Ridges of their Wavelet Transforms. IEEE Trans. Signal Proc. IEEE Trans. Sign. Proc.45 (1997) 2586 - 2590.

  51. (with W.L. Hwang and B. Torresani): Identification of Chirps with the Continuous Wavelet Transforms. in Wavelets and Statistics eds A. Antoniadis & G. Oppenheim}, Lect. Notes in Statist. 103 95-109.

  52. (with W.L. Hwang and B. Torresani): Multiridge Detection and Time-Frequency Reconstructions. IEEE Trans. Signal Proc. 47, (1999) 480-492.

  53. (with A. Wang): Comparison Tests for the Spectra of Dependent Multivariate Time Series. in Progress in Probab. Vol. 39, Stochastic Modelling in Physical Oceanography, eds R. Adler, P. Mueller and B. Rozovskii. pp. 69-88, Birkhauser NY.

  54. (with L. Hudgins): Wavelet Denoising of EEG Signals and Identification of Evoked Responses. in Proc. Intern. SPIE Conf. Signal Processing and Image Analysis, San Diego July 1994, 2303 91-104.

  55. (with S. Grishin and S.A. Molchanov): Massively Parallel Simulations of Motions in a Gaussian Velocity Field. in Progress in Probab. Vol. 39, Stochastic Modelling in Physical Oceanography, eds R. Adler, P. Mueller and B. Rozovskii. pp. 47-68, Birkhauser NY.

  56. (with F. Viens and S.A. Molchanov): Sharp Upper Bound for a Parabolic Stochastic Partial Differential Equation. Random Oper. and Stochastic Equ. 4 (1996) 43-50.

  57. (with F. Viens): Almost Sure Exponential Behavior of a Stochastic Anderson Model with Continuous Space Parameter. Stochastics and Stoc. Rep. 62 (1998) 251-273.

  58. (with S. Grishin, S.A. Molchanov and L.Xu): Surface Stretching for Ornstein Uhlenbeck Velocity Fields. Electron. Comm. Probab. 2 (1997) 1-11.

  59. (with L. Xu): Large Deviations and Exponential Decay of the Magnetization in a Gaussian Random Field. Probab. Theory and Related Fields 106 (1996) 233-257.

  60. (with L. Xu): Homogenization for Time Dependent Gaussian Velocity Fields. Ann. Appl. Probab. 7 (1997) 265-279.

  61. (with L. Xu): Diffusive Scaling Limit for a System with Finite Range Random Interaction, Commun. Math. Phys. 188 (1997) 565-584.

  62. (with S. Zhong) Nonlinear Diffusion and Adaptive Smoothing Respecting Feature Direction. IEEE Trans. Image Proc. Special Issue PDE's and Geometry Driven Diffusion in Image Analysis. 7 (1997) 353-358.

  63. (with S. Zhong) Interior Point Methods for the Enhancement of Acoustic Images of the Sea Bottom, Proc. of SPIE 3079 (1997) 132-137.

  64. Renormalization Theories for Incompressible Flows with Gaussian Statistics in Monte Carlo Simulations in Oceanography 'Aha Huliko'a Proc. (1997) University of Hawaii. 71-81.

  65. (with A. Al-khalidy, M. Noori, Z. Hou, S. Yamamoto, A. Masuda and A. Sone) A Study of Health Monitoring Systems of Linear Structures Using Wavelet Analysis, Proceedings of the ASME PV&P Conf. PVP-Vol. 347, (1997) 49-58.

  66. (with L. Xu) Calibrating Arbitrage-Free Stochastic Volatility Models by the Relative Entropy Method, in Proceedings 3rd Ascona Seminar on Stoch. Analysis, Random Fields and Appl. Birkhauser.

  67. (with Ph. Briand) BSDE's with Polynomial Growth Generators. J. of Applied Math. and Stochastic Analysis 12 (1999)

  68. (with M. Tehranchi) A Characterization of Hedging Portfolios for Interest Rate Contingent Claims, Annals of Applied Probability 14 (2004) 1267-1294

  69. (with V. Durrleman) Pricing and Hedging Spread Options, SIAM Review 45 (2004) 627 - 685

  70. (with D. Villani) Monte Carlo Helps with Pricing, Environmental Finance June (2003) 20 - 21

  71. (with D. Villani and R. Ghigliazzi) A Discrete Affair, Energy Risk Nov (2003) 68 - 70

  72. (with S. Grishin and S.A. Molchanov) Asymptotics for the Boundary Parabolic Anderson Problem in a Half Space. Random Operators and Stochastic Equations, 12 (2004) 105 - 128

  73. (with P. Diko) Pricing Precipitation Based Derivatives. International Journal of Theoretical and Applied Finance, 7 (2005) 959-988.

  74. (with V. Durrleman) Pricing and Hedging Multivariate Contingent Claims, The Journal of Computation Finance 9(2) (2005) 1-25.

  75. (with N. Touzi) Optimal Multiple Stopping and Valuation of Swing Options, Mathematical Finance 18 (2008) 239-268.

  76. (with M. Ludkowski) Spot Convenience Yield Models for the Energy Markets. Contemporary Mathematics, 351 (2004) 65-80

  77. (with M. Ludkovski) Commodity Forwards with Partial Observation and Exponential Utility. International Journal of Theoretical and Applied Finance,

  78. (with L. Wang) Monte Carlo Malliavin Sensitivity Computations for Solutions of SPDE's. SIAM J. Applied Mathematics 69 (2009) 1682-1711

  79. (with M. Ludkovski) Pricing Asset Scheduling Flexibility using Optimal Switching. Applied Mathematical Finance, 15 (5), (2008) 405–447.

  80. (with M. Ludkovski) Valuation of Energy Storage: an Optimal Switching Approach. Quantitative Finance,10 (4), (2010) 359–374.

  81. (with S. Dayanik) Optimal Multiple Stopping of Linear Diffusions. Mathematics of Operations Research, 33 (2) (2008) 446–460.

  82. (with S. Nadtochiy) Local Volatility Dynamic Models. Finance and Stochastics, 13 (2009) 1-48.

  83. (with A. Danilova): Consistency of the Geometric Brownian Motion Model of Stock Prices with Asymmetric Information. Mathematical Finance} (submitted Oct. 2007) “manuscript under revision”

  84. (with J.P. Fouque and D. Vestal): Interacting Particle Systems for the Computation of CDO Tranche Spreads with Rare Defaults. Finance and Stochastics, 13 (2009) 613-633.

  85. (with M. Fehr and J. Hinz) Optimal Stochastic Control and Carbon Price Formation. SIAM J. on Control and Optimization, 48 (2009) 2168-2190.

  86. (with M. Fehr, J. Hinz and A. Porchet) Market Design for Emissions Markets Trading Schemes. SIAM Review, 52 (2010) 403-452.

  87. (with S. Nadtochiy) An Infinite Dimensional Stochastic Analysis Approach to Local Volatility Dynamic Models Communications on Stochastic Analysis, 2 (2008) 109–123.

  88. (with S. Cr'epey) Importance Sampling and Interacting Particle Systems for the Estimation of Markovian Credit Portfolio Loss Distributions. International. J. of Theoretical and Applied Finance, 13 (4) (2010), 577–602.

  89. (with M. Fehr and J. Hinz) Properly Designed Emissions Trading Schemes can Work! (submitted for publication)

  90. (with M. Fehr) The Clean Development Mechanism and CER Price Formation in the Carbon Emissions Markets, Seminar on Stocahstic Analysis, Random Fields and Applications. VI Ascona Conference, May 2008. Ascona CH, eds R. Dalang, M. Dozzi, F. Russo. Birkhauser (2010) 341 – 384.

  91. (with S. Nadtochiy) Tangent Levy Market Models. Finance and Stochastics, 16 (1) (2012) 63–104.

  92. (with S. Nadtochiy) Tangent Models as a Mathematical Framework for Dynamic Calibration. International J. of Theoretical and Applied Finance, 14 (2011) 107 – 135.

  93. (with J. Hinz) Risk-Neutral Modeling of Emission Allowance Prices and Option Valuation. Management Science, 57 (8) (2011) 1453 – 1468.

  94. (with M. Fehr) Auctions and Relative Allocation Mechanisms for Cap-and-Trade Schemes (2011) submitted for publication.

  95. (with F. Delarue, G-E. Espinosa and N. Touzi) Singular forward-backward stochastic differential equations and emissions derivatives. Annals of Applied Probability, 23 (3) (2013) 1086-1128.

  96. (with J. Yang) Predatory Trading: a Game on Volatility and Liquidity. Quantitative Finance}, (Sep. 2011) under revision

  97. (with Y. Sun) Implied and Local Correlations from Spread Options. Applied Mathematical Finance, (July 2012) (under revision)

  98. (with F. Delarue) Singular FBSDEs and Scalar Conservation Laws Driven by Diffusion Processes. Theory of Probability and Related Fields (2012) appeared on line

  99. (with F. Delarue and A. Lachapelle) Control of McKean-Vlasov Dynamics versus Mean Field Games. Mathematical and Financial Economics, 7 (2012)131-166.

  100. (with J. Hinz) Least Squares Monte Carlo Approach to Convex Control Problems. IEEE Transactions on Automatic Control, (2011) under revision.

  101. (with F. Delarue) Probabilistic Analysis of Mean Field Games. SIAM Journal on Control and Optimization, 51 (4) (2013) 2705 - 2734.

  102. (with M. Coulon and D. Schwarz) Electricity Price Modeling and Asset Valuation: a Multi-Fuel Approach. Mathematical and Financial and Economics, 7 (2012) 167-202.

  103. (with M. Coulon and D. Schwarz) The valuation of clean spread options: linking electricity, emissions and fuels. Quantitative Finance,12 (12) (2012) 1951-1965

  104. (with F. Delarue) Control of McKean Vlasov Dynamics. Annals of Probability (2013) submitted for publication.

  105. (with K. Webster) High Frequency Market Making. Mathematical Finance (2012) submitted for publication

  106. (with F. Delarue) Mean Field Forward-Backward Stochastic Differential Equations. Electronic Communications in Probability, 18 (2013) article #68, 1-15.