师资队伍

              
  

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

 

论文:

[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.      

专著:

Shige Peng, Nonlinear Expectations and Stochastic Calculus under Uncertainty,with Robust CLT and G-Brown Motion, Springer,2019

 

 

 

 



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