彭实戈 院士
中国科学院院士
山东大学数学学院教授,博士生导师
[1] The Existence Problem of Optimal Control for Nonlinear Processes Applied Mathematics and Mechanics, 4:6, 1983 1983.
[2] Etude de Perturbations Singulières en Controle Optimal Deterministe Thèse de Docteur de 3ème Cycle de Université de Paris, Faculté de Dauphine, 1985.
[3] Singular perturbations in optimal control problems Commande des systèmes complexes technologiques, 20, 359-381, 1986.
[4] Etude de Perturbations et d’homogéneisation des Systèmes Stochastiques et des Systemes Periodiques Thèse de Doctorat, Université de Provence, 1986.
[5] Analyse Asymptotique et Problème Homogéneisé en Controle Optimal Avec Vibrations Rapides SIAM.J. of Control and Optimization, 27:4, 673-696,1989.
[6] The Maximum Principle 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] On Hamilton-Jacobi-Bellman Equation with Stochastic Coefficients in Proceeding of the Annual Meeting on Control Theory and It’s Application,1989.
[8] A General Stochastic Maximum Principle for Optimal Control Problems SIAM. J. of Control and Optimization, 28:4, 966-979, 1990.
[9] 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, 724-732, 1990.
[10] Adapted Solution of a Backward Stochastic Differential Equation Systems and Control Letters, 14, 55-61, 1990.
[11] Maximum Principle for Semilinear Stochastic Evolution Control Systems Stochastics and stochastics Reports, 33, 159-180, 1990.
[12] Positivity-Perserving Mapping and Its Application Lecture Notes in Control and Enformathion Sciences, Edited by M. Thoma and A. Wyner, Proceedings of the IFIP WG 7.2 Working Conference Shanghai China, Springer-Verlag,1990.
[13] A New Type of Singularly Perturbed Diffusion Processes and It’s Application Asymptotic Analysis, 5, 173-186, 1991.
[14] Maximum Principle for Optimal Control of Generalized Systems Acta. Automatica Sinica, 18:1, 17-23, 1991.
[15] A Generalized Hamilton-Jacobi-Bellman Equation Lecture Notes in CIS, 184, Li Yong eds, 126-134, Springer-Verleg, Berlin, 1991.
[16] Probabilistic Interpretation for Systems of Quasilinear Parabolic Partial Differential Equations Stochastics and Stochastics Report, 37, 61-74, 1991.
[17] Adapted Solution of a Backward Semilinear Stochastic Evolution Equation Stochastic Analysis and Applications, 9(4), 445-459, 1991.
[18] Determination of a Controllable Set for a Controlled Dynamic System J. Austral. Math. Soc. Ser. B33, 164-179, 1991.
[19] Maximum Principle for Semilinear Stochastic Evolution Systems Chin. Ann. of Math., 12B:3, 256-266, 1991.
[20] A New Type of Singularly Perturbed Diffusion and Its Applications Asymptotic Analysis, 5, 173-186, 1991.
[21] Stochastic Hamilton-Jacobi-Bellman Equations SIAM J. Control 30(2), 284-304, 1992.
[22] Document de Synthese Pour I’Habilitation a Diriger des Recherches University de Provence, 1992.
[23] A Generalized Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equation Stochastics and Stochastics Reports, 38, 119-134, 1992.
[24] Maximum Principle for Optimal Control of Nonlinear Generalized Systems-Infinite Dimensional Case ACTA Math. Appl. Sinica, 15(1), 99-104, 1992.
[25] Backward Stochastic Differential Equations and Quasilinear Partial Differential Equations Lecture Notes in CIS, 176, 200-217, Springer, 1992.
[26] A Nonlinear Feynman-Kac Formula and Application Control Theory Stochasdic Analysis and Applications, S.Chen and J. Yong Ed., 173-184, World Scientific, Singapore, 1992.
[27] New Development in Stochastic Maximum Principle and Related Backward Stochastic Differential Equations In proceedings of 31st CDC Conference, Tucson, 1992.
[28] H∞ type Optimal Control Ploblem Control Theory Stochasdic Analysis and Applications, S.Chen and J. Yong Ed., 79-95, World Scientific, Singapore, 1992.
[29] Positivity-Preserving Mapping and Its Application Chen Yong Ed. 279-189, World Scientific, Singapore, 1992.
[30] A Global Representation of All Solutions to a Nonlinear Equation and It’s Applications Chin. Ann. of Math., 13B (4), 455-462, 1992.
[31] Backward Stochastic Differential Equations and Applications in Optimal Control Appl. Math. Optim, 27:125-144,1993.
[32] Some Backward Stochastic Differential Equations with non-Lipschitz Coefficients Proc. Conf. Metz, 1993.
[33] Backward Stochastic Differential Equation and Exact Controllability of Stochastic Control Systems Progress in Natural Science, 4:3, 274-284, 1994.
[34] Backward Doubly Stochastic Differential Equations and Systems of Quasilinear SPDEs Probab. Theory Relat. Fields. 98, 209-227, 1994.
[35] BSDE and Exact Controllability of Stochastic Control Systems Progress in Natural Science, 4:3, 274–284, 1994.
[36] A Linear Quadratic Optimal Control Problem with Disturbances An algebric Riccati equation and differential games approach, 30: 267-305, 1994.
[37] Forward and Backward Stochastic Differential Equations Probab. Theory Related Fields, 103:273-283, 1995.
[38] Backward Stochastic Differential Equation in Finance Mathematical Finance, 1997, 7, 1-71.
[39] 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.
[40] BSDEs with Continuous Coeffcients and Stochastic Differential Games Stochastic Differential Equations, Pitman Research Notes in Math. Series, No.364, El Karoui Mazliak edit, 115-128,1997.
[41] Topics in Stochastic Analysis Ch.2: BSDE and Stochastic Optimizations (Chinese vers.), Science Publication, 1997.
[42] Backward Stochastic Differential Equations and Applications Advances in Mathematics (Chinese version), 26:2, 97-112, 1997.
[43] Backward Stochastic Differential Equations in Finance Mathematical Finance, 7:1, 1-71,1997.
[44] Reflected Solutions of Backward SDE’s, and Related Obstacle Problems for PDE’s Mat The Annals of Prob., 25:2, 702-737, 1997 (with El Karoui,Kapoudjian,Pardoux,Quenez)
[45] A Stability Theorem of Backward Stochastic Differential Equations and Its Application C. R. Acad. Sci. Paris, t.324, Série I, 1059-1064, 1997.
[46] Backward Stochastic Differential Equations and Stochastic Optimizations (Chinese vers.) Topics in Stochastic Analysis, Ch.2,,85–138, Science Publication, 1997.
[47] A Nonlinear Doob-Meyer type Decomposition and it's Application SUT Journal of Mathematics (Japan), 34, No.2, 197-208, 1998.
[48] Existence of Stochastic Control under State Constraints C. R. Acad. Sci. Paris, t. 327, Serie I, 17-22, 1998.
[49] A Decomposition Theorem of g-Martingales SUT Journal of Mathematics, 34:2, 197-208, 1998.
[50] Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control SIAM. J. of Control and Optim. , 37:3, 825-843, 1999.
[51] Monotonic Limit Theorem of BSDE and Nonlinear Decomposition Theorem of Doob-Meyer's Type Proba. Thoery Related Fields, 113, 473-499, 1999.
[52] Stationary Backward Stochastic Differential Equations and Associated Partial Differential Equations Proba. Theory Related Fields, 115, 383-399, 1999.
[53] Infinite Horizon Boundary Value Problems and Applications J. Diff. Equ. , 155, 405-422, 1999.
[54] Duplicating and Pricing Contingent Claims with Constrained Portfolios Progress in Natural Science, 1999.
[55] A General Downcrossing Inequality for g-Martingales Statistics and Prob. Letters, 45, 1999.
[56] Ergodic Backward SDE and Associated PDE Progress in Probability, 45, 73-85, 1999.
[57] Duplicating and Pricing Contingent Claims in Incomplete Markets Pacific Economic Review, 4:3, 237-260, 1999.
[58] A Linear Approximation Algorithm Using BSDE Pacific Economic Review, 4:3, 285-291, 1999.
[59] Problem of Eigenvalues of Deterministic and Stochastic Hamiltonian Systems with Boundary Conditions Journal of Fudan University (Natural Science), 38(4), 374-378, 1999.
[60] Duality of Stochastic Hamiltonian Systems Journal of Fudan University (Natural Science), 38, 474-476, 1999.
[61] Open Problem on Backward Stochastic Differential Equations Control of Distributed Parametre and Stochastic Systems, (with S.Chen, X.Li, J.Yong, X. Zhou),Kluwer Academic Publishers, 265-274, 1999.
[62] Probabilistic Approach to Homogenization of Viscosity Solution of Parabolic PDEs Nonlinear Differ. Equ. Appl. 6, 395-411, 1999.
[63] Infinite Horizon Forward-Backward Stochastic Differential Equations Stochastic Processes and Their Applications, 85, 75-92, 2000.
[64] Probabilitic approach to homogenization of viscosity solutions of parabolic PDEs Nonlinear differ. equa. Appl. , 6, 395-411, 1999.
[65] Problem of Eigenvalues of Stochastic Hamiltonian Systems with Boundary Conditions Stochastic Processes and Their Applications, 88, 259-290, 2000.
[66] A Converse Comparison Theorem for BSDEs and Related Properties of g-Expectation Electron Comm. Prob. , 5, 101-117, 2000.
[67] Smallest g-Supersolution for BSDE with Continuous Drift Coefficients Chin. Ann. Of Math., 21B:3, 359-366, 2000.
[68] A General Downcrossing Inequality for g-Martingales Statistics & Probability Letters, 46, 169–175, 2000.
[69] A Stochastic Laplace Transform for Adapt Processes and Related BSDEs Optimal Control and Partial Differential Equations, J.L. Menaldi et (Eds.), 283-292, IOS Press, Amsterdam, 2001.
[70] Continuous Properties of g-Martingales Chin. Ann. of Math. , 22b:1, 115-128, 2001.
[71] A General Converse Comparison Theorem for Backward Stochastic Differential Equations C. R. Acad. Sci. Paris, t. 333, Serie I, 557-581, 2001.
[72] A Dynamic Maximum Principle for the Optimization of Recursive Utilities under Constraints The Annals of Applied Probability, 11(3), 664-693, 2001.
[73] Filtration-Consistent Nonlinear Expectations and Related g-Expectations Probab. Theory Relat. Fields, 123, 1-27, 2002.
[74] Infinite Horizon Backward Stochastic Differential Equation and Exponential Convergence Index Assignment of Stochastic Control Systems Automatica, 38, 1417-1423, 2002.
[75] Risk-Sensitive Dynamic Portfolio Optimization with Partial Information on Infinite Time Horizon The Annals Applied Probability, 12(1), 173-195, 2002.
[76] A Type of Time-Symmetric Forward-Backward Stochastic Differential Equations C. R. Acad. Sci. Paris, I 336(9): 773-778, 2003.
[77] Determination of a Controllable Set for a Class of Nonlinear Stochastic Control System Optim. Control Appl. Meth., 24:173-181, 2003.
[78] Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims Acta Mathematicae Applicatae Sinica, English Series, 20:2, 1-24, 2004.
[79] Nonlinear Expectations, Nonlinear Evaluations and Risk Measures K. Back et al.: LNM 1856, M. Frittelli and W. Runggaldier(Eds.), Springer-Verlag Berlin Heidelberg,165-253, 2004.
[80] Dynamical Evaluations C. R. Acad. Sci. Paris, Ser. I 339, 585-589, 2004.
[81] Nonlinear Expectation, Nonlinear Evaluations and Risk Measurs Stochastic Methods in Finance Lectures, C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy 2003, 143–217, LNM 1856, Springer-Verlag, 2004 (Edit. M. Frittelli and W. Runggaldier).
[82] Nonlinear Expectations and Nonlinear Markov Chains Chin. Ann. Math., 26B:2,159-184, 2005.
[83] The Smallest g-Supermartingale and Reflected BSDE with Single and Double L2 Obstacles Ann. I. H. Poincaré-PR, 41, 605-630, 2005.
[84] Necessary and Sufficient Condition for Comparison Theorem of 1-Dimensional Stochastic Differential Equations Stochastic Processes and Their Application, 116, 379-380, 2006.
[85] On The Comparison Theorem for Multidimensional BSDEs C. R. Acad. Sci. Paris, Ser. I 343, 135-140, 2006.
[86] The Viability Property of Controlled Jump Diffusion Processes Acta Mathematica Sinica, English Series, Vol. 24, No. 8, pp. 1351–1368Aug., 2008.
Shige Peng, Nonlinear Expectations and Stochastic Calculus under Uncertainty,with Robust CLT and G-Brown Motion, Springer,2019
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