Peng Shige
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Chinese mathematician
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Peng Shigemathematics Degrees
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Group Theory
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Number Theory
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Mathematics
Peng Shige's Degrees
- Bachelors Mathematics Peking University
- Masters Mathematics Peking University
- PhD Mathematics Peking University
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Why Is Peng Shige Influential?
(Suggest an Edit or Addition)According to Wikipedia, Peng Shige is a Chinese mathematician noted for his contributions in stochastic analysis and mathematical finance. Biography Peng Shige was born in Binzhou and raised in Shandong, while his parents' hometown is Haifeng County in south-eastern Guangdong, he is a grandnephew of the famous revolutionary Peng Pai, and his grandfather is also recognized a "revolutionary martyr" by the nation. He went to a countryside working with farmers as an "Educated youth" from 1968 to 1971, and studied in the Department of Physics, Shandong University from 1971 to 1974 and went to work at the Institute of Mathematics, Shandong University in 1978. In 1983 he took an opportunity to enter Paris Dauphine University, France under the supervision of Alain Bensoussan, who was a student of Jacques-Louis Lions. He obtained his PhDs from Paris Dauphine University in 1985 and from University of Provence in 1986. Then he returned to China and did postdoctoral research at Fudan University before becoming a professor at Shandong University in 1990. In 1992 he was awarded the Habilitation à Diriger des Recherches by the University of Provence. He was promoted to Distinguished Professor of the Ministry of Education of China in 1999.
Peng Shige's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Adapted solution of a backward stochastic differential equation (1990) (2598)
- Backward Stochastic Differential Equations in Finance (1997) (2191)
- Backward stochastic differential equations and quasilinear parabolic partial differential equations (1992) (834)
- Reflected solutions of backward SDE's, and related obstacle problems for PDE's (1997) (732)
- A general stochastic maximum principle for optimal control problems (1990) (718)
- G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type (2006) (653)
- Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths (2008) (555)
- Probabilistic interpretation for systems of quasilinear parabolic partial differential equations (1991) (537)
- Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation (2006) (503)
- Nonlinear Expectations and Stochastic Calculus under Uncertainty (2010) (461)
- Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control (1999) (439)
- Solution of forward-backward stochastic differential equations (1995) (381)
- Backward stochastic differential equations and applications to optimal control (1993) (366)
- Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type (1999) (347)
- Backward doubly stochastic differential equations and systems of quasilinear SPDEs (1994) (344)
- Nonlinear Expectations, Nonlinear Evaluations and Risk Measures (2004) (324)
- A Generalized dynamic programming principle and hamilton-jacobi-bellman equation (1992) (320)
- Mean-field backward stochastic differential equations and related partial differential equations (2007) (303)
- Stochastic Hamilton-Jacobi-Bellman equations (1992) (283)
- Mean-field backward stochastic differential equations: A limit approach (2007) (258)
- Filtration-consistent nonlinear expectations and related g-expectations (2002) (248)
- Mean-field stochastic differential equations and associated PDEs (2014) (235)
- Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations (2009) (219)
- G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty (2007) (206)
- Anticipated backward stochastic differential equations (2007) (205)
- A New Central Limit Theorem under Sublinear Expectations (2008) (177)
- Adapted solution of a backward semilinear stochastic evolution equation (1991) (170)
- Stopping times and related Itô's calculus with G-Brownian motion (2009) (166)
- A dynamic maximum principle for the optimization of recursive utilities under constraints (2001) (163)
- On representation theorem of G-expectations and paths of G-Brownian motion (2009) (162)
- Representation of the penalty term of dynamic concave utilities (2008) (162)
- A Converse Comparison Theorem for BSDEs and Related Properties of g-Expectation (2000) (160)
- Backward stochastic differential equations driven by G-Brownian motion (2012) (147)
- NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS (2005) (147)
- Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations (2006) (142)
- Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion (2012) (139)
- The smallest g-supermartingale and reflected BSDE with single and double L2 obstacles (2005) (131)
- Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011) (126)
- Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims (2004) (125)
- A New Kind of Accurate Numerical Method for Backward Stochastic Differential Equations (2006) (120)
- Risk-Sinsitive Dynamic Portfolio Optimization with Partial Information on Infinite Time Horizon (2002) (109)
- BSDE, path-dependent PDE and nonlinear Feynman-Kac formula (2011) (99)
- Maximum principle for semilinear stochastic evolution control systems (1990) (93)
- Law of large numbers and central limit theorem under nonlinear expectations (2007) (79)
- Infinite horizon forward–backward stochastic differential equations (2000) (77)
- On the comparison theorem for multidimensional BSDEs (2006) (76)
- Dynamically Consistent Nonlinear Evaluations and Expectations (2005) (73)
- Open Problems on Backward Stochastic Differential Equations (1998) (71)
- Existence of stochastic control under state constraints (1998) (70)
- Backward Stochastic Differential Equation Driven by Fractional Brownian Motion (2009) (68)
- Note on Viscosity Solution of Path-Dependent PDE and G-Martingales (2011) (66)
- A type of time-symmetric forward–backward stochastic differential equations (2003) (64)
- A general downcrossing inequality for g-martingales (2000) (60)
- Maximum Principle for Backward Doubly Stochastic Control Systems with Applications (2010) (60)
- A complete representation theorem for G-martingales (2012) (60)
- Error estimates of the $\theta$-scheme for backward stochastic differentialequations (2009) (51)
- Stochastic optimization theory of backward stochastic differential equations with jumps and viscosity solutions of Hamilton–Jacobi–Bellman equations (2009) (49)
- Representation Theorems for Quadratic F-Consistent Nonlinear Expectations (2007) (44)
- A general converse comparison theorem for backward stochastic differential equations (2001) (42)
- Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs (1999) (40)
- Reflected BSDE with a constraint and its applications in an incomplete market (2010) (39)
- Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations (2011) (38)
- Modelling Derivatives Pricing Mechanisms with Their Generating Functions (2006) (35)
- Stochastics An International Journal of Probability and Stochastic Processes : formerly Stochastics and Stochastics Reports (2014) (34)
- Stochastic Methods in Finance (2004) (33)
- Limit theorems with rate of convergence under sublinear expectations (2017) (33)
- Convergence of solutions of discrete reflected backward SDE’s and simulations (2008) (33)
- Tightness, weak compactness of nonlinear expectations and application to CLT (2010) (32)
- Stationary backward stochastic differential equations and associated partial differential equations (1999) (30)
- Terminal perturbation method for the backward approach to continuous time mean-variance portfolio selection (2008) (30)
- $G$-expectation weighted Sobolev spaces, backward SDE and path dependent PDE (2013) (29)
- G-Lévy processes under sublinear expectations (2009) (29)
- On controllability for stochastic control systems when the coefficient is time-variant (2010) (29)
- Three Algorithms for Solving High-Dimensional Fully Coupled FBSDEs Through Deep Learning (2019) (28)
- Maximum principle for optimal control of stochastic system of functional type (1996) (28)
- Reflected solutions of backward stochastic differential equations driven by G-Brownian motion (2018) (26)
- Infinite horizon backward stochastic differential equation and exponential convergence index assignment of stochastic control systems (2002) (25)
- Nonlinear Stochastic Differential Games Involving a Major Player and a Large Number of Collectively Acting Minor Agents (2013) (24)
- Jensen’s inequality for g-convex function under g-expectation (2008) (24)
- Sublinear Expectations and Martingales in discrete time (2011) (24)
- Improving Value-at-Risk Prediction Under Model Uncertainty (2018) (24)
- A stability theorem of backward stochastic differential equations and its application (1997) (23)
- A linear approximation algorithm using BSDE (1999) (20)
- Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions (2000) (19)
- The viability property of controlled jump diffusion processes (2008) (19)
- Singular perturbations in optimal control problems (1986) (16)
- BSDEs with random default time and their applications to default risk (2009) (16)
- Stochastic calculus with respect to G-Brownian motion viewed through rough paths (2015) (16)
- Optimal unbiased estimation for maximal distribution (2016) (16)
- Duplicating and Pricing Contingent Claims in Incomplete Markets (1999) (15)
- Some Estimates for Martingale Representation under G-Expectation (2010) (15)
- Constrained BSDE and Viscosity Solutions of Variation Inequalities (2007) (15)
- Martingale problem under nonlinear expectations (2012) (13)
- CONTINUOUS PROPERTIES OF G-MARTINGALES (2001) (13)
- BSDEs with random default time and related zero-sum stochastic differential games (2010) (11)
- A hypothesis-testing perspective on the G-normal distribution theory (2019) (9)
- Extended conditional G-expectations and related stopping times (2013) (9)
- Maximum principle for viscosity solutions on Riemannian manifolds (2008) (8)
- Supermartingale Decomposition Theorem under G-expectation (2017) (8)
- Stein Type Characterization for $G$-normal Distributions (2016) (7)
- New developments in stochastic maximum principle and related backward stochastic differential equations (1992) (7)
- A linear quadratic optimal control problem with disturbances—An algebraic Riccati equation and differential games approach (1994) (7)
- On the set of solutions of a BSDE with continuous coefficient (2007) (7)
- Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle (2020) (6)
- Reflected BSDE driven by G-Brownian motion with an upper obstacle (2017) (6)
- G-Gaussian processes under sublinear expectations and $ q $-Brownian motion in quantum mechanics (2011) (6)
- Constrained BSDEs, viscosity solutions of variational inequalities and their applications (2013) (6)
- The Pricing Mechanism of Contingent Claims and its Generating Function (2012) (6)
- Filtration Consistent Nonlinear Expectations (2001) (6)
- A generalized Hamilton-Jacobi-Bellman equation (1991) (6)
- The Numerical Algorithms and simulations for BSDEs (2006) (6)
- Maximum principle for stochastic optimal control with non convex control domain (1990) (5)
- Asymptotic analysis and the homogeneous problem in optimal control with rapid vibrations (1989) (5)
- Reflected Solutions of BSDEs Driven by G-Brownian Motion (2017) (4)
- Ergodic Backward SDE and Associated PDE (1999) (4)
- A stochastic Laplace transform for adapted processes and related BSDEs (2001) (4)
- Viability property on Riemannian manifolds (2009) (4)
- SMALLEST g-SUPERSOLUTION FOR BSDE WITH CONTINUOUS DRIFT COEFFICIENTS (2000) (4)
- Distributional uncertainty of the financial time series measured by $G$-expectation (2020) (3)
- A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs (2022) (3)
- Risk-Sensitive Optimal Investment Problems with Partial Information on Infinite Time Horizon (2001) (3)
- Nonlinear Expectations and Risk Measures (2003) (3)
- On Representation Theorem of G G-Expectations and Paths (2009) (3)
- Numerical Algorithms for BSDEs: Convergence and Simulations (2006) (3)
- Solving Stochastic Optimal Control Problem via Stochastic Maximum Principle with Deep Learning Method (2020) (3)
- Wong–Zakai Approximation for Stochastic Differential Equations Driven by G-Brownian Motion (2020) (2)
- G-Stochastic Calculus Viewed through Rough Paths and the Norris Lemma in G-framework (2015) (2)
- Determination of a controllable set for a class of non‐linear stochastic control systems (2003) (2)
- Wong-Zakai Approximation through Rough Paths in the G-expectation Framework (2015) (2)
- A control method for solving high-dimensional Hamiltonian systems through deep neural networks (2021) (2)
- Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear Decomposition (2006) (2)
- Infinite Horizon Boundary Value Problems and Applications (1999) (2)
- Numerical Algorithms for 1-d Backward Stochastic Differential Equations: Convergence and Simulations (2006) (2)
- A universal robust limit theorem for nonlinear L\'evy processes under sublinear expectation (2022) (2)
- Determination of a controllable set for a controlled dynamic system (1991) (1)
- Maximally distributed random fields under sublinear expectation (2022) (1)
- Autoregressive models of the time series under volatility uncertainty and application to VaR model. (2020) (1)
- Deep learning method for solving stochastic optimal control problem via stochastic maximum principle (2020) (1)
- Wong-Zakai Approximation for SDEs Driven by $G-$Brownian Motion. (2015) (1)
- Spatial and temporal white noises under sublinear G-expectation (2018) (1)
- A Generalized Central Limit Theorem with Applications to Econometrics and Finance (2008) (1)
- ANTICIPATED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS 1 (2009) (1)
- A new type of singularly perturbed diffusion and its applications (1991) (1)
- Real options, ambiguity, risk and insurance : world class university program in financial engineering, Ajou University, volume two (2013) (1)
- On the exit times of SDEs driven by $G$-Brownian motion (2018) (1)
- Law of Large Numbers and Central Limit Theorem Under Probability Uncertainty (2019) (1)
- Stochastic Differential Equations (2019) (1)
- J un 2 01 0 Strong laws of large numbers for capacities (2010) (0)
- Capacity and Quasi-surely Analysis for G-Brownian Paths (2019) (0)
- Parabolic Equations with Quadratic Growth in $$\mathbb {R}^{n}$$ (2018) (0)
- G-Martingale Representation Theorem (2019) (0)
- A Note on $G$- Optimal Stopping Problems (2012) (0)
- Brownian Motion under Nonlinear Expectation and related BSDE (2012) (0)
- G-Brownian Motion and Itô’s Calculus (2019) (0)
- Martingale problem under nonlinear expectations (2017) (0)
- Stochastic calculus with respect to G-Brownian motion viewed through rough paths (2016) (0)
- Testing and finding the generating functions of an option pricing mechanism through market data (2006) (0)
- Spatial and temporal white noises under sublinear G-expectation (2019) (0)
- Wong–Zakai Approximation for Stochastic Differential Equations Driven by G-Brownian Motion (2020) (0)
- Backward Stochastic Differential Equations and Related Control Problems (2015) (0)
- A biographical note and tribute to xunjing li on his 80th birthday (2015) (0)
- BSDE, path-dependent PDE and nonlinear Feynman-Kac formula (2015) (0)
- Some Further Results of Itô’s Calculus (2019) (0)
- Sublinear Expectations and Risk Measures (2019) (0)
- Martingale Problems under Nonlinear Expectation (2012) (0)
- A DECOMPOSITION THEOREM OF g-MARTINGALES * (1998) (0)
- Reflected Solutions of BSDEs Driven by $\textit{G}$-Brownian Motion (2018) (0)
- PR ] 1 5 M ay 2 01 8 On the exit times for SDEs driven by G-Brownian motion (2018) (0)
- A novel control method for solving high-dimensional Hamiltonian systems through deep neural networks (2021) (0)
- G-Martingales and Jensen’s Inequality (2019) (0)
- Backward StochasticDifferential Equations and RelatedControl Problems (2015) (0)
- Special issue dedicated to Alain Bensoussan on the occasion of his 80th birthday: Preface (2022) (0)
- Deep Learning in Finance (2023) (0)
- Imbalanced binary classification under distribution uncertainty (2022) (0)
- Report on Testing and Finding the Generating Functions g of an Option Pricing Mechanism through Market Data (2009) (0)
- About the editors and authors (2020) (0)
- Reflected solutions of backward stochastic differential equations driven by G-Brownian motion (2017) (0)
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