New Research


2008/02/01

Mathematical Finance, Stochastic Analysis and Stochastic Control.


Professor Hideo Nagai, Associated Professor Arturo Kohatsu-Higa, Assistant Professor Takashi Tamura

The Nagai Laboratory (part of the Graduate of Engineering Science, Division of Mathematical Science for Social Systems) is a group working in the mathematical analysis, foundation and construction of mathematical models describing real situations in financial markets. In particular, our areas of research and training are within (but not restricted) to Financial Engineering and the required fundamental theories such as Stochastic Analysis and Stochastic Control between others.

In the present situation, global markets determine the future economic environment. It is clear that in order to study them we need to study its complex random structure. The understanding of this structure helps avoiding as much as possible the manageable risks. To achieve this goal one needs to build appropriate mathematical models, analyze them and test them in reality. The theoretical tools that are important to achieve this goal are stochastic analysis, stochastic control and filtering theory. In order to test these models, the proper numerical analysis and simulation is also required.

For example, the derivatives market was created in order to reduce some of the risks involved in stock trading. In order to evaluate if the market prices are correct and to price complex derivative products one needs to use the most recent techniques of stochastic analysis and stochastic control. Some of the quantities appearing in such a situation are expressed as expectations of functionals of stochastic processes. Recently, infinite dimensional analysis techniques such as Malliavin Calculus are used to evaluate these quantities.

Our group is also devoting big efforts into the analysis of optimal portfolio policy choice theory. To study this problem we use advanced results in Stochastic Analysis, Stochastic Control and Filtering Theory. For example, in order to study an optimal choice in portfolio optimization, one usually solves a non-linear partial differential equation known as the Hamilton-Jacobi-Bellman equation. At present we are currently researching on large deviation control problems minimizing investment risks in asset allocation by solving the H-J-B equations.

Our research group essentially uses the theory of stochastic differential equations to build on the analysis of the market behavior. In order to enter this area of research it is necessary to have a strong background and interest in probability theory, real and complex analysis and overall in mathematics. Although, it is also important to develop computer skills that will help in testing the mathematical results obtained. Previous students that have graduated from our laboratory presently work at various financial companies or economic research institutions (private and governmental) as well as universities.

We welcome all the students that are interested in participating in this exciting group. Most of our recent research as well as educational activities are summarized in our lab’s webpage (in Japanese).
Starting in 2006 we have also been an active party in the establishment of the Center for The Study of Finance and Insurance at Osaka University. For more information about the center please direct your browser to (http://www-csfi.sigmath.es.osaka-u.ac.jp/)


Aida & Nagai Laboratory URL(JAPANESE ONLY)
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