Abstract

An important assumption in deep learning and related fields that has long been widely criticized, but is still frequently applied in theory and practice, is the IDD of sample data (both training and test data)., especially when one needs to obtain the expected value of the sample or its function, i.e., key statistics such as expected utility, expected error, and expected risk exposure. But on the other hand, the research and analysis of some typical financial data at home and abroad show that the assumption often used in the financial field has led to some obvious errors. The research shows that we need to use more universal nonlinear expectation theory and algorithms, so as to scientifically and steadily eliminate these accumulation errors and risks. This report will analyze and explain why nonlinear expectation algorithms can be used more accurately to calculate the uncertainty behind the data. 

Biography

Academician Peng is an eminent mathematician based at Shandong University where he serves as the Director of the Mathematics Institute and the Finance Institute.

Prof. Peng obtained his bachelor degree in physics from Shandong University in 1974, and his Ph.D. in mathematics from Paris Dauphine. He has been a professor with Shandong University since 1990. Among the numerous honors that he has received in his career, we mention his plenary lecture at the 2010 ICM, plenary lecture at the 2015 ICIAM, and his election to the Chinese Academy of Sciences in 2005.  Indeed, he is the sole ICM plenary speaker from China so far.  He is highly regarded for his exceptional contributions to mathematical sciences, his invention of backward stochastic differential equations and nonlinear expectation in particular. They have become indispensable tools in several branches of mathematics.