The Association of Mathematical Finance Laboratory (hereinafter called “AMFiL”) was established in April of 2017 to encourage education and research in mathematical finance and related fields and to serve as a base for AMFiL members to promote their research.

Broadly speaking, mathematical finance is an area of research in which securities and financial markets are analyzed using mathematical methods such as probability theory and statistics. There are similar research fields such as financial engineering and econometrics. However, I personally regard the field of mathematical finance to be that which pursues mathematical strictness due to its nature as a theoretical study; it represents an aspect of physics that explains social phenomena in the securities and financial markets.

While the members of AMFiL are pursuing research activities of their own in mathematical finance and related areas, we are planning to produce a blog that introduces basic knowledge in mathematics and modern portfolio theory—which is necessary for research in mathematical finance—and a variety of topics related to Fintech (finance + technology). We would like to post understandable and easy-to-read articles, not only for the readers who are interested in mathematical finance, but also for a broad range of potential readers.

Recent years have seen both the development of information technology (IT) and several financially stressful events; as a result, practices in financial products trading and risk management have become increasingly complex. The securities trading sector actively employs high frequency trading (HFT), in which orders are expected to be placed in milliseconds, microseconds, or even nanoseconds by taking advantage of computer technologies. The use of HFT signals a high possibility that the very structure of securities markets will change drastically. The construction and development of the derivative pricing theory are major research achievements in the fields of mathematical finance and financial engineering. However, the mathematical methods required in pricing models or risk management for complicated derivatives are becoming highly sophisticated, particularly in light of a series of financial crises such as the subprime mortgage crisis and the financial crisis of 2007-08. Furthermore, we believe that the construction of basic theories in the securities and financial markets plays a very important role in securing the order and integrity of the market, particularly as utilization of Fintech progresses with the following: development of machine learning, democratization, the birth of cryptocurrency by blockchain technologies, and the rapid expansion of the market size. To construct these basic theories, theoretical and empirical researchers and practitioners across various disciplines must work together in the spirit of unity by sharing information and enhancing mutual understanding.

AMFiL’s business must also be useful for the good of many people. Rather than staying only in the theoretical research field of mathematical finance, we are determined to conduct business with a broad perspective, working in collaboration with the activities of other researchers and business people in various fields.


Takashi Kato, Ph.D.