Annals of Mathematical Sciences and Applications

Volume 5 (2020)

Number 2

Statistical models and stochastic optimization in financial technology and investment science

Pages: 317 – 345



Tze L. Lai (Department of Statistics, Stanford University, Stanford, California, U.S.A.)

Shih-Wei Liao (Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan)

Samuel P. S. Wong (Department of Statistics, Chinese University of Hong Kong; and Department of Statistics and Actuarial Science, University of Hong Kong)

Huanzhong Xu (ICME, Stanford University, Stanford, California, U.S.A.)


In the decade since the global financial crisis and the Great Recession that followed, the financial technology—or FinTech—revolution has transformed financial markets and services through the automation of trading and risk management, among other things. The “ABCD” of cutting-edge FinTech are AI (Artificial intelligence), Blockchains, Cloud computing and big Data. We first review these technologies of modern FinTech and some of the underlying mathematical foundations. We then describe new statistical models and stochastic optimization methods in FinTech and investment science.


blockchains, cryptographic hash functions, collision resistance, empirical Bayes, portfolio optimization

T.L. Lai is partially supported by NSF DMS-1407828 and DMS-1811818.

Received 23 June 2020

Accepted 1 October 2020

Published 13 October 2020