Peng Shige is a Chinese mathematician noted for his contributions in stochastic analysis and mathematical finance.

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Education

He 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. He obtained his Doctor of Philosophy from Paris Dauphine University in 1985 and from University of Provence in 1986.

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Career

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. 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 (Cheung Kong Scholarship Programme) in 1999.

Professor Peng generalized the stochastic maximum principle in stochastic optimal control. In a paper published in 1990 with Étienne Pardoux, Peng founded the general theory of backward stochastic differential equations (BSDEs), introduced by Jean-Michel Bismut in 1973.

Soon Feynman–Kac type connections of BSDEs and certain kinds of elliptic and parabolic partial differential equations, e.g., Hamilton–Jacobi–Bellman equation, were obtained, where the solutions of these PDEs can be interpreted in the classical or viscosity senses. As a particular case the solution of the Black–Scholes equation can be represented as the solution of a simple linear BSDE, which can be regarded as a starting point of the BSDEs" applications in mathematical finance.

A type of nonlinear expectation, called the g-expectation, was also derived from the theory of BSDEs.

General theories of nonlinear expectations were developed later. These have various applications in utility theory, and the theory of dynamic risk measures.

## Membership

Chinese Academy of Sciences.