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Shige Peng

Other affiliations: Rutgers University, University of Provence, Fudan University  ...read more
Bio: Shige Peng is an academic researcher from Shandong University. The author has contributed to research in topics: Stochastic differential equation & Nonlinear expectation. The author has an hindex of 56, co-authored 143 publications receiving 18621 citations. Previous affiliations of Shige Peng include Rutgers University & University of Provence.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors considered the problem of finding an adapted pair of processes with values in Rd and Rd×k, respectively, which solves an equation of the form: x(t) + ∫ t 1 f(s, x(s), y(s)) ds + ∪ t 1 [g(m, x, s, g(m)) + y(m)] dW s = X.

2,812 citations

Journal ArticleDOI
TL;DR: In this article, different properties of backward stochastic differential equations and their applications to finance are discussed. But the main focus of this paper is on the theory of contingent claim valuation, especially cases with constraints.
Abstract: We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b).

2,332 citations

Journal ArticleDOI
TL;DR: In this article, reflected solutions of one-dimensional backward stochastic differential equations are studied and the authors prove uniqueness and existence both by a fixed point argument and by approximation via penalization.
Abstract: We study reflected solutions of one-dimensional backward stochastic differential equations. The “reflection” keeps the solution above a given stochastic process. We prove uniqueness and existence both by a fixed point argument and by approximation via penalization. We show that when the coefficient has a special form, then the solution of our problem is the value function of a mixed optimal stopping–optimal stochastic control problem. We finally show that, when put in a Markovian framework, the solution of our reflected BSDE provides a probabilistic formula for the unique viscosity solution of an obstacle problem for a parabolic partial differential equation.

781 citations

Journal ArticleDOI
TL;DR: The maximum principle for nonlinear stochastic optimal control problems in the general case was proved in this article, where the control domain need not be convex, and the diffusion coefficient can contain a control variable.
Abstract: The maximum principle for nonlinear stochastic optimal control problems in the general case is proved. The control domain need not be convex, and the diffusion coefficient can contain a control variable.

725 citations


Cited by
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Book
01 Dec 1992
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
Abstract: Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.

4,042 citations

Book ChapterDOI
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

2,446 citations

Journal ArticleDOI
TL;DR: In this article, different properties of backward stochastic differential equations and their applications to finance are discussed. But the main focus of this paper is on the theory of contingent claim valuation, especially cases with constraints.
Abstract: We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b).

2,332 citations