New Research


2010/10/01

Mathematical Finance

Toward further development after crisis

Research Group of Mathematical Modeling in Finance.Professor: Jun Sekine,Assistant Professor: Yukio

1) Group information.
 a) Main research topics: Mathematical Finance (Sekine). Probability Theory related to Statistical Physics (Nagahata).
 b)Education and Activity (e.g., student advising, research guidance, research seminar and workshop): We are cooperating with other research groups in Area of Mathematicaland Statistical Finance and CSFI (Center for the Study of Finance and Insurance).

2) Focusing on MF(Mathematical Finance): overview and present status.
 In MF, mathematical models of financial markets are constructed and analyzed. Mathematical outputs are fed back to real financial market problems and used to try to explain and interpret them. Rapid development of information and computer technology from 80\'s enables us to have applied theoretical results in this field to real market problems. Explosive growth of derivatives (i.e., financial derivative securities) is a typical example.
 Currently, in MF, high-level mathematical theories and technologies have been intensively applied and they are now playing important roles: for example,stochastic differential equation (and related Ito\'s stochastic calculus), stochastic control, viscositysolution theory on partial differential equation, theory on infinite dimensional calculus(e.g., Malliavin calculus), etc.
 Through the recent world-wide financial crisis, we have learned that it is very dangerous to recklessly apply \"standard\" theory of MF, in which many idealizations and restrictions are assumed. (Although, theoretically, we have understood very well the limitation of such a standard theory.) For further developments of MF, not only individual efforts of all researchers, but also serious discussions and collaborations among researchers in different fields, such as practitioners, economists, and mathematical scientists, are now emphasized.

3) Examples of current research topics:
 i) Risk-sensitive portfolio optimization
 ii) Large deviations controls
 iii) Application of dynamic portfolio insurance techniques
 iv) Stochastic correlation factor model
 v) Information(filtering)-based asset pricing

 We welcome all the students who are interested in participating in this exciting group.


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