Nonlinear Expectation and Applications.

Nonlinear expectation, first developed by Prof. Shige Peng, is an important mathematical tool to study Knightian uncertainty and financial risk. Since the beginning of this century, Nonlinear Expectation has attracted more interest from academic researches and a lot of progress has been made from the theoretical point of view. Since the assumptions of the identical and independent distribution of the data may not be satisfied in traditional sense, there is great potential in measuring and managing financial risk based on the Nonlienar Expecation theory. Meanwhile, the i.i.d. condition is also frequently violated in machine learning. Leveraging nonlinear expectation theory, Michael Xuan and his collaborators have constructed a general robust machine learning framework. The Smale Institute is committed to driving the adoption and development of nonlinear expectation and robust machine learning across even broader domains.

Shige Peng and Michael Xuan