SELECTED PLENARY, KEYNOTE AND MAJOR INVITED TALKS

1. Plenary lecture "Law of Large Number and Central Limit Theorem under Uncertainty, the Related New Itô’s Calculus and Applications to Risk Measures", 1st PRIMA Congress, July 06-10, 2009 UNSW, Sydney, Australia

2. Plenary lecture: “Backward Stochastic Differential Equation, nonlinear expectations and their applications”, ICM 2010, Hyderabad, India, August 19-27.

           Notes (click to download)

3. Plenary lecture "Covering the Uncertainty of Probability Distributions by Nonlinear Expectation, Nonlinear PDE and BSDE", The 8th ICIAM, Aug. 10-14, 2015 Beijing.

   
   

SHORT COURSES AND SERIES OF LECTURES

1. “Nonlinear Expectations, Nonlinear Evaluations and Risk Measures” Lectures given at the C.I.M.E.-E.M.S. Summer School, Main lecturer of CIME “Stochastic Methods in Finance” , July 7-12, 2003 in Bressanone/Brixen (Italy).

           Notes (click to download)

2. Course Bachelier, “Nonlinear Expectations and Risk Measures” (4 courses) Institut Henri Poincarre, april 2005.

3. Minicourse on “Backward Stochastic Differential Equations and Nonlinear Expectations ” FORSCHUNGINSTITUT FUR MATHEMATIK, ETH, Zurich from January 16 to February 03, 2005

4. 3 Lectures on “G-Expectation, G-Brownian and Related Stochastic Calculus” in 2nd Workshop on “Stochastic Equations and Related Topics” July 23–29, 2006, Jena, Germany.

5. “G–Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty” Course in CSFI, Osaka University, May 17-June, 2007.

6. Minerva Foundation Lecturer (course): “Coherent and Convex Risk Measures, and the Related Time-Consistent Nonlinear Expectations" Oct. 17-Nov. 27, 2008, Columbia University, New York.

7. Nonlinear Expectations and Stochastic Calculus under Uncertainty, Course in Spring School “Stochastic Control in Finance", European ITN Marie Curie Project, 08-23 March 2010, Roscoff, France.

8. Mini-Course: “Lectures on Nonlinear Expectations and Nonlinear Martingales”, Spring School of Roscoff, March 06-15, 2012.

9. Global Scholar Short courses: “Nonlinear Expectation Theory and Backward Stochastic Differential Equations”, Princeton University, March-May, 2012-2014.

10. Mini-course: “Controls, Games under Uncertainty using G-Expectations”, Research School of Controllability of Deterministic and Stochastic Systems and its Appl., July, 2012, Iasi, România.

11. OMI Mini-course: “Backward Stochastic Differential Equations and Nonlinear Expectations”, January 17-24, 2013, in Man-Oxford Institute , Oxford University.

Publications

[1] (with Z. H. Chen) The existence problem of optimal control for nonlinear processes, Applied Mathematics and Mechanics, 4: 6, 1983.

[2] (with A. Bensoussan) Singular perturbations in optimal control problems, Commande des systèmes complexes technologiques, 20, 359-381, 1986.

[3] Etude de Perturbations Singulières en Contrôle Optimal Deterministe, Thèse de Docteur de 3ème Cycle de Université de Paris, Faculté de Dauphine, 1985.

[4] Etude de Perturbations et d'homogéneisation des Systèmes Stochastiqueset des Systemes Periodiques, Thèse de Doctorat, Université de Provence, 1986.

[5] Analyse Asymptotique et Problème Homogéneisé en Contrôle Optimal Avec Vibrations Rapides, SIAM.J. of Control and Optimization, 27:4, 673-696, 1989.

[6] (with Y. Hu and X. Li) The Maximum Priciple for Stochastic Optimal Control Problems with Mixed Constraints, (in Chinese), in Proceeding of the Annual meeting on Control Theory and It's Applications, 1988.

[7] A General Stochastic Maximum Principle for Optimal Control Problems, SIAM J. Cont. 28: 4, 966-979, 1990.

[8] Maximum Principle for Stochastic Optimal Control with Nonconvex Control Domain, in Analysis and Optimization of Systems, A. Bensoussan J. L. Lions eds. Lecture Notes in Control and Information Sciences, 144, (1990), 724-732.

[9] A New Type of Singularly Perturbed Diffusion Processes and It's Application, Asymptotic Analysis, 5, 173-186, 1991.

[10] (with X. Li) Maximum Principle for Optimal Control of Generalized Systems, in Acta. Automatica Sinica, 18: 1, 17-23, 1991.

[11] Adapted Solution of a Backward Stochastic Differential Equation, Systems and Control Letters, 14, 55-61, 1990, (with E. Pardoux).

[12] On Hamilton-Jacobi-Bellman Equation with Stochastic Coeffcients, in Proceeding of the Annual Meeting on Control Theory and It's Applications, 1989.

[13] A Generalized Hamilton-Jacobi-Bellman Equation, Lecture Notes in CIS, 184, Li Yong eds, 126{134, Springer-Verleg, Berlin, 1991.

[14] (with Y. Hu) Maximum Principle for Semilinear Stochastic Evolution Control Systems, in Stochastics, 33 159-180, 1990.

[15] Probabilistic Interpretation for Systems of Quasilinear Parabolic Partial Differential Equations, Stochastics, 37, 61-74, 1991.

[16] (with Y. Hu) Adapted Solution of Backward Stochastic Evolution Equation, Stochastic Analysis and Applications, 9(4), 445-459, 1991.

[17] (with J. Yong) Determination of a Controllable Set for a Controlled Dynamic System, in J. Austral. Math. Soc. Ser.B 33, 164-179, 1991.

[18] (with Hu Y.) Maximum Principle for Semilinear Stochastic Evolution System, Chin. Ann. Math., 12B:3, 256-266, 1991.

[19] Stochastic Hamilton-Jacobi-Bellman Equations, SIAM Control 30(2), 284-304, 1992.

[20] Document de Synthese Pour l'Habilitation a Diriger des Recherches, University de Provence, 1992.

[21] A Generalized Dynamic Programming Principle and Hamilton-Jacobi-Bellmen equation, Stochastics, 38, 119-134, 1992.

[22] (with Hu Y. and Li X.) Maximum Principle of Optimal Control for Non-linear Generalized Systems, In nite Dimensional Case, ACTA Math.Appl. Sinica, 15(1), 99-104 1992.

[23] (with E..Pardoux) Backward Stochastic Differential equations and Quasi-linear Parabolic Partial Differential Equations, Lecture Notes in CIS176, 200-217, Springer 1992.

[24] A Nonlinear Feynman-Kac Formula and Applications, Proceedings of Symposium of System Sciences and Control theory, Chen Yong ed. 173-184, World Scienti c, Singapore, 1992.

[25] New Development in Stochastic Maximum Principle and Related Backward Stochastic Differential Equations, in proceedings of 31st CDC Conference, Tucson 1992.

[26] (with S. Chen X. Li, J. Yong) H1 type Optimal Control Problem, Chen Yong Ed. 79-95, World Scienti c, Singapore, 1992.

[27] Positivity-Preserving Mapping and Its Application, (with S. Chen) ChenYong Ed. 279-289, World Scienti c, Singapore, 1992.

[28] A Global Representation of All Solutions to a Nonlinear Equation and It's Applications, Chin. Ann. of Math., 13B(4), 455{462, 1992 (with J. Yong).

[29] Backward Stochastic Di erential Equation and It's Application in Optimal Control, in Appl. Math. Optim 27:125-144, 1993.

[30] (with E.Pardoux) Backward Doubly Stochastic Differential equations and Systems of Quasilinear Parabolic SPDEs, Proba. Theory Related Fields. 98 209-227, 1994

[31] BSDE and Exact Controllability of Stochastic Control Systems, Progress in Natural Science, 4 3, 274-284, 1994.

[32] (with N. El Karoui and M.-C., Quenez) Backward Stochastic Differential Equation in Finance, Mathematical Finance, 1997, 7, 1-71.

[33] Backward SDE and Related g-Expectation, in Backward Stochastic Differential Equations, Pitman Research Notes in Math. Series, No.364, El Karoui Mazliak edit. 141-159, 1997.

[34] (with E. Pardoux) Some Backward stochastic Differential Equations withnon-Lipschitz Coeffcients, in Proc. Conf. Metz, 1993.

[35] (with Hamadene and Lepeltier) BSDEs with Continuous Coeffcients and Stochastic Differential games, in Backward Stochastic Differential Equa-tions, Pitman Research Notes in Math. Series, No.364, El Karoui Mazliakedit. pp115-128, 1997 .

[36] (with Y. Hu) Forward and Backward Stochastic Differential Equations, Probab. Theory Related Fields, 103:273-283, 1995.

[37] Backward Stochastic Differential Equations and Applications, in Advances in Mathematics (Chinese version), 26, 2, 97-112, 1997.

[38] (with El Karuoi, Kapoudjian, Pardoux and Quenez) Refected Solutions of Backward SDE's and Related Obstacle Problems for PDE's, The Annalsof Prob., 25, 2, 702-737, 1997.

[39] (with Y. Hu) A Stability Theorem of Backward Stochastic Differential Equations and Applications, C.R.Acad. Sci. Paris, t.324, Serie I, 1059-1064, 1997.

[40] (with Z. Chen) A Nonlinear Doob-Meyer type Decomposition and its Application. SUT Journal of Mathematics (Japan), 34, No.2, 197-208, 1998.

[41] (with Wu Zheng) Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control, SIAM Control, 1999.

[42] (with Buckdahn, Quincampoix and Rainer) Existence of Stochastic Control under State Constraints, C.R.Acad. Sci. Paris, t. 327, Serie I, 17-22, 1998.

[43] Monotonic Limit Theorem of BSDE And Nonlinear Decomposition Theorem Of Doob-Meyer'S Type, Proba. Theory Related Fields, 113, 473-499, 1999.

[44] (with R. Buckdahn) Stationary Backward Stochastic Differential Equations and Associated Partial Differential Equations, Proba. Theory Related Fields, 115, 383-399, 1999.

[45] (with Y. F. Shi) In nite horizon boundary value problem and applications, J. Diff. Equ. 155, 405-422, 1999.

[46] (with Feng Yang) Duplicating and Pricing Contingent Claims with Constrained Portfolios, Progress in Natural Science, 1999.

[47] (with Z. Chen) A General Downcrossing Inequality for g-Martingales, Statistics and Prob. Letters, 45, 1999.

[48] (with R. Buckdahn) Ergodic Backward SDE and Associated PDE, Progresses in Probability, 45, 73-85, 1999.

[49] (with Yang Feng) Duplicating and Pricing Contingent Claims in Incomplete Markets, Paci c Economic Review, 4(3) 237-260, 1999.

[50] A Linear Approximation Algorithm Using BSDE, Paci c Economic Review, 4(3) 285-291, 1999.

[51] Problem of Eigenvalues of Deterministic and Stochastic Hamiltonian Systems with Boundary Conditions, Journal of Fudan University (Natural Science), 38, 374-378, 1999.

[52] Duality of Stochastic Hamiltonian Systems, Journal of Fudan University(Natural Science), 38, 474-476, 1999.

[53] Open Problems on Backward Stochastic Differential Equations, in pp265-274, Control of Distributed Parametre and Stochastic Systems, edit. S.Chen, X. Li J. Yong and X.Y. Zhou, Kluwer Academic Publishers, 1999.

[54] (with Yufeng Shi) In nite Horizon Forward{Backward Stochastic Differential Equations, Stochastic Processes and Their Applications, 85, 75-92, 2000.

[55] Problem of Eigenvalues of Stochastic Hamiltonian Systems with Boundary Conditions, Stochastic Processes and Their Applications, 88, 259-290, 2000.

[56] (with Ph. Brian, F. Coquet, Y. Hu, J. Memin) A converse comparison theore for BSDEs and related proberties of g-expectation, Electron Comm. Prob., (5),101-117, 2000.

[57] (with R. Buckdahn and Ying Hu) Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs, Nonlinear differ. equa. appl.6 395-411, 1999.

[58] (with R. Buckdahn and Y. Hu) Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs, in NoDEA, Nonlinear Differential Equations and Applications, Birkhauser Verlag, 395 - 411, 1999.

[59] (with Shuping Chen, Xunjing Li and Jiongmin Yong) A linear quadratic optimal control problem with disturbances, an algebric Riccati equation and differential games approach, 30:267-305 1994.

[60] A Stochastic Laplace Transform for Adapted Processes and Related BSDEs, in Optimal Control and Partial Differential Equations, J.L. Menaldiet al. (Eds.) 283-292, IOS Press, Amsterdam, 2001. 

[61] (with Z. Chen) Continuous Properties of g-Martingales, Chin. Ann. of Math. 22b:1, 115-128, 2001.

[62] (with F. Coquet, Y. Hu, J. Memin) A general converse comparison theore for backward stochastic differential equations, C.R.Acad. Sci. Paris, t. 333, Serie I, 557-581, 2001.

[63] (with F. Coquet, Y. Hu and J. Memin) Filtration Consistent Nonlinear Expectations and Related g-Expectations, Probab. Theory Relat. Fields 123, 1-27, 2002.

[64] (with Zengjing Chen) A general downcrossing inequality for g-martingales, Statistics & Probability Letters, 46, 169-175, 2000.

[65] (with Liu Yazeng) In nie horizon backward stochastic differential equation and exponential convergence index assignment of sthastic control systems, Automatica 38 (2002) 1417-1423.

[66] (with Hideo Nagai) Risk-sensitive dynamic portfolio optimization with partial information on in nite time horizon, The Annals of Applied Probability, Vol. 12, No. 1173-195 (2002).

[67] (with Yufeng Shi) A type of time symmetric forward backward stochastic diferential equations, C.R. Acad. Sci., I 336(9): 773-778, 2003.

[68] Filtration consistent nonlinear expectations and evaluations of contingent claims, Acta Mathematicae Applicatae Sinica, English Series Vol. 20, No. 2, 1-24, 2004.

[69] Nonlinear expectations and nonlinear Markov chains, Chin. Ann. Math. 26B:2(2005),159-184.

[70] Dynamical evaluations, C. R. Acad. Sci. Paris, Ser. I 339 585-589, 2004.

[71] (with M. Xu) Smallest g-supermartingales and related refected BSDEs with single and double barriers, Ann. I. H. Poincaré - PR 41 (2005) 605-630.

[72] (with Zhu, X.) Necessary and suffcient condition for comparison theorem of 1-dimensional stochastic differential equations, Stochastic Processes and their Applications 116 (2006) 370-380.

[73] (with Ying Hu) On the comparison theorem for multidimensional BSDEs, C. R. Acad. Sci. Paris, Ser. I 343 (2006) 135-140.

[74] G-expectation, G{Brownian motion and related stochastic calculus of Itô’s type, in Stochastic Analysis and Applications, The Abel Symposium 2005, Abel Symposia ·2, Edit. Benth et. al., 541-567, Springer-Verlag, 2006.

[75] Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation, Stochastic Processes and their Applications 118(12), 2008, 2223-2253.

[76] (with JI Shaolin) Terminal perturbation method for the backward approach to continuous time mean(R)Cvariance portfolio selection, Stochastic Processes and their Applications 118, 952(R)C967, 2008.

[77] (with HU Ying, MA, Jin & YAO Song) Representation theorems for quadratic F-consistent nonlinear expectations, in Stochastic Processes and their Applications, 118, 1518(R)C1551, 2008.

[78] (with HU Yaozhong) Backward stochastic differential equation driven by fractional Brownian motion, SIAM J.Control Optim., 48 (2009), no.3, 1675-1700.

[79] Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Sci. China Ser. A 52 (2009), no.7, 1391-1411.

[80] (with Hu, Ming-shang) On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math. Appl. Sin. Engl. Ser. 25 (2009), no.3, 539-546.

[81] (with LI Juan) Stochastic optimization theory of backward stochastic differential equations with jumps and viscosity solutions of Hamilton(R)CJacobi(R)CBellman equations, in Nonlinear Analysis 1776(R)C1796, 2009.

[82] (with YANG Zhe) Anticipated backward stochastic differential equations, Ann. Probab. 37 (2009), no.3, 877-902.

[83] (with Buckdahn, Rainer; Djehiche, Boualem; Li, Juan) Mean- eld backward stochastic di erential equations: a limit approach, Ann. Probab. 37(2009), no. 4, 1524-1565

[84] (with Yuecai HAN and Zhen WU) Maximum principle for backward doubly stochastic control systems with applications, SIAM J. Control Optim., 48(7) (2010), 4224-4241.

[85] (with Guangyan Jia) Jensen's inequality for g-convex function under g-expectation,

[86] Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications, lecture of plenary talk of ICM2010, in Proceedings of the International Congress of Mathematicians Hyderabad, India, 2010.

[87] (with Freddy Delbaen and Emanuela Rosazza Gianin) Representation of the penalty term of dynamic concave utilities, in Finance and Stochastics, 0949-2984 (2010).

[88] (with Li Xinpeng) Stopping times and related Itô’s calculus with G-Brownian motion, Stochastic Processes and their Applications 121 (2011). 1492-1508.

[89] (with Hu Mingshang, Ji Shaolin and Song Yongsheng) Backward stochastic differential equations driven by G-Brownian motion, Stochastic Processes and their Applications, 2012 , 124 (1) :759-784.

[90] (with Hu Mingshang, Ji Shaolin and Song Yongsheng) Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion, Stochastic Processes and their Applications, 2012 , 124 (2) :1170-1195.

[91] (with R. Buckdahn and J. Li ) Nonlinear stochastic differential games involving a major player and a large number of collectively acting minor agents, SIAM Journal on Control and Optimization, 2013, 52 (1) :451-492.

[92] (with Y. Song and J. Zhang) A complete representation theorem for G-martingales, Stochastics An International Journal of Probability and Stochastic Processes 2013, 86 (4) :609-631.

[93] (with Yongsheng Song) G-expectation weighted Sobolev spaces, backward SDE and path dependent PDE, Journal of the Mathematical Society of Japan, 2015 , 67 (4).

[94] (with F.L. Wang) BSDE, path-dependent PDE and nonlinear Feynman-Kac formula, Science China-Mathematics, 2016, 59 (1): 19-36.

[95] Mean- eld stochastic differential equations and associated PDEs, (with Rainer Buckdahn, Juan Li and Catherine Rainer) Annals of Probability, 2017.

[96] (with Xu Mingyu) Constrained BSDEs, viscosity solutions of variational inequalities and their applications, Mathematical Control and Related elds, 2017, 3 (2) :233-244.

[97] Theory, methods and meaning of nonlinear expectation (Survey in Chinese), SCIENTIA SINICA Mathematica 47(10) 1223-1254, 2017.

[98] Refected solutions of backward stochastic differential equations driven by G-Brownian motion (with Hanwu LI and Abdoulaye SOUMANA HIMA), Science in China, Mathematics, 61(1), pp1-26, 2018.

[99] (with JI Xiaojun) Spatial and temporal white noises under sublinear G-expectation, Science China, Mathematics, 63(1), 61-82 (2020).