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



现任职务:
教育部“****”****
山东大学泰山学堂院长
普林斯顿大学全球****



荣誉与奖励:
第十届华罗庚数学奖，2011
全国先进工作者，2010
山东省科学技术最高奖，2003
国家自然科学二等奖，1995
教育部科技进步一等奖，1994


研究方向:
Nonlinear expectations and Stochastic calculus
Mathematical finance: Option pricing and risk measurement
Theory of stochastic differential games
Recursive Utilities under Risk and Uncertainty
Stochastic and deterministic optimal control systems
Controllability of stochastic control systems
Stochastic and deterministic partial differential equations
Singular perturbations method for stochastic systems




联系方式:
通讯地址：山东省济南市 山大南路27号 山东大学数学学院（250100）
办公电话：+86- 传真：+86-
E-mail：peng@sdu.edu.cn

---

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



现任职务:
教育部“****”****
山东大学泰山学堂院长
普林斯顿大学全球****



荣誉与奖励:
第十届华罗庚数学奖，2011
全国先进工作者，2010
山东省科学技术最高奖，2003
国家自然科学二等奖，1995
教育部科技进步一等奖，1994


研究方向:
Nonlinear expectations and Stochastic calculus
Mathematical finance: Option pricing and risk measurement
Theory of stochastic differential games
Recursive Utilities under Risk and Uncertainty
Stochastic and deterministic optimal control systems
Controllability of stochastic control systems
Stochastic and deterministic partial differential equations
Singular perturbations method for stochastic systems




联系方式:
通讯地址：山东省济南市 山大南路27号 山东大学数学学院（250100）
办公电话：+86- 传真：+86-
E-mail：peng@sdu.edu.cn

---

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

研究方向:
Nonlinear expectations and Stochastic calculus
Mathematical finance: Option pricing and risk measurement
Theory of stochastic differential games
Recursive Utilities under Risk and Uncertainty
Stochastic and deterministic optimal control systems
Controllability of stochastic control systems
Stochastic and deterministic partial differential equations
Singular perturbations method for stochastic systems

主持承担的科研项目:
国家重点发展基础研究计划（973项目）：金融风险控制中的定量分析与计算，2007-2011
国家高等学校学科创新引智计划项目（111 计划）：金融风险控制中的定量分析和计算创新引智基地，2012-2016
国际学术会议报告:
27. Backward Stochastic Differential Equations, Nonlinear Expectation and Their Applications,
第26届国际数学家大会一小时大会报告, 2008年8月19日至27日, 印度
26. 倒向随机微分方程、非线性数学期望和G-布朗运动，
第14次院士大会，数理学部学术年会报告，2008年6月26日
25. Plenary Speaker: Risk measure and central limit theorem under sublinearexpectation,
《International Conference on Stochastic Analysis and Related Fields》,
April 7–11, 2008 随机分析及相关领域国际会议，华中科技大学，武汉
24. Plenary Speaker: A New Central Limit Theorem under Sublinear Expectation and G-Brownian Motion,
《Stochastics and Real World Models》,
Bielefeld May 5th, 2008
23. G-Expectations and BSDE Driven by G-Brownian Motion,
《5th Colloquium on Backward Stochastic Differential Equations, Finance and Applications, Le Mans, June 18 - 20, 2008》, 第一个Planary Speaker
22. G-Normal Distribution, G-Brownian Motion and Financial Risk 《IMSChina International Conference on Statistics and Probability》,
Zhejiang University, Hangzhou, June, 2008.
21. Dynamic Risk Measures in Finance, Robust Central Limit Theorem andG-Brownian Motion,
Lanzhou, Aug. 11, 2007.
20. 《Dynamic Risk Measures in Finance, Robust Central Limit Theorem and G-Brownian Motion》,
Banff, July 2007.
19. “G–Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty”
Lectures in CSFI, Osaka University, May 17-June
18. Academic Activities on Stochastic Analysis and its Applications,
Invited lectures: “G-Brownian motion and related central limit theorem, (Lecture I, April 16, Lecture II, April 18), Institute of Applied Mathematics,
AMSS, Beijing.
17. Plenary talk: Conference on Probability and Statistics,
Xuzhou, 2007.
16. Second Sino-German Meeting on Stochastic Analysis,
Invited talk: “G-Brownian motion, Central Limit Theorem under Sublinear Expectations and Risk Measures”
March, 19-23, 2007, Beijing .
15. Workshop on Mathematical Finance and Stochastic Control,
Invited talk:“Risk Measures with G-expectations and G-Brownian motions”,
August 24-27, 2006, Kyoto.
14. International Workshop on Mathematical Finance and Insurance, Lijiang,
“G-Expectation, G-Brownian and Related Stochastic Calculus” ,China,
May 27 – June 3, 2006.
13. 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.
12. Workshop on Risk Measures, 6-7,
Invited talk: “G-Expectation, G-Measure of Risk and Related Stochastic Calculus”
July 2006, Evry, France.
11. Intenational Workshop on Mathematical Finance and Insurance,
May 27-June 3, 2006, Lijiang, China.
10. The 2005 Abel Symbosium, Stochastic Analysis and Applications -A Symposium in Honor of Kiyosi It?,
July 29 - August 4, Oslo, Norway.
9. Workshop on Financial Engineering and Risk Management, Institute of Math. Chinese Academic of Science,
08-10, Dec. 2005.
8. 4th Colloqium on Backward Stochastic Differential Equations and Applications,
Fudan, Shanghai, 2005.
7. Workshop “Stochastic Equations and Related Topics”
Jena, March 28 – April 1, 2005.
6. Cours Bachelier, “Nonlinear Expectations and Risk Measures” (4 courses) Institut Henri Poincarre,
avril 2005.
5. Main Organizer: Satelite Conference of World Conference of Mathematicians: Backward Stochastic Differential Equations and Applications,
2002, Weihai.
4. Main speaker: “International Symposium on Stochastic Process and Applications to Mathematical Finance”,
March, 6–7, 2002, Ritsmeikan, Japan.
3. “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).
2. International Conference on Applied Statistics, Actuarial Science and Financial Mathematics,
Invited talk: “Recent developments in BSDE and nonlinear expectations”,
Dec. 17-19, 2002, Hong Kong.
1. Planary talk: International Workshop “Recent Development in Derivative Securities Markets”,
June, 6–8, 1998, Hong Kong.

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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:

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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

预印本:
[1]　G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type,arXiv:math/** v2　
[2]　 Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation, arXiv:math/** v2　
[3]　Modelling Derivatives Pricing Mechanisms with Their Generating Functions, arXiv:math/** v1　
[4]　Numerical Algorithms for 1-d Backward Stochastic Differential Equations: Convergence and Simulations, arXiv:math/** v4　
[5]　Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear Decomposition, arXiv:math/** v4　
[6]　Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations　
[7]　Representation Theorems for Quadratic -Consistent Nonlinear Expectations,arXiv:0704.1796 v1　
[8]　Anticipated Backward Stochastic Differential Equations,arXiv:0705.1822 v1　
[9]　Mean-Field Backward Stochastic Differential Equations: A Limit Approach,arXiv:0711.2162 v2　
[10]　Mean-Field Backward Stochastic Differential Equations and Related Partial Differential Equations,arXiv:0711.2167 v1　
[11]　G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty,arXiv:0711.2834 v1　
[12]　Constrained BSDE and Viscosity Solutions of Variation Inequalities,arXiv:0712.0306 v2　
[13]　Jensen's Inequality for g-Convex Function under g-Expectation,arXiv:0802.0373 v1　
[14]　Representation of the penalty term of dynamic concave utilities,arXiv:0802.1121 v1,　
[33]　Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion, arXiv:1212.5403