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 (including nonlinear expectation) of backward stochastic differential equations (BSDEs), though linear BSDEs had been introduced by Jean-Michel Bismut in 1973.[5] Soon Feynman–Kac type connections of BSDEs and certain kinds of elliptic and parabolic partial differential equations (PDEs), 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.
In 2011, he was appointed as "Global Scholars" for academic years 2011–2014 by Princeton University, hosted by the university's departments of mathematics, operations research and financial engineering, and the Program in Applied and Computational Mathematics, as he "is a global leader in the field of probability theory and financial mathematics."[11][12][13]
In March 2015, as one of six or seven nominees, Peng was nominated for Abel Prize by Norwegian mathematician Bernt Øksendal.[5]
