Researcher's Information

Professor

KOHATSU-HIGA, Arturo

Mathematics

Stochastic Analysis, Monte Carlo Methods, Stochastic Differential Equations

My research interests are centered on various applied and theoretical aspects of simulation for stochastic systems which evolve with time. 
In particular, we are interested in stochastic equations of different types. These equations may have various applications in finance, engineering and physics. One of the challenges consists in studying their theoretical properties of these methods and obtaining efficient simulation methods. Therefore students working with me may do either theoretical studies related with these problems or simulation studies which have a strong mathematically oriented theoretical basis. We sometimes also try to test newly proposed simulation methods and find some theoretical basis to explain their behavior. The goal is to obtain fast and accurate methods that can be used in various practical problems and therefore there is a strive to achieve some generality over particularity. 
Usually, students working on simulations will be proficient in C programming or other similar languages such as scilab, octave, R or python. On the theoretical side, we request basic knowledge and interest in either probability theory, stochastic process or Monte Carlo methods. 
Our students, usually interact with the group of mathematical finance where they can also experience the direct feeling of applications to real problems. Therefore our group is very active, we encourage discussions between students, visitors and professors. We have frequent seminars, many times given by visitors from various countries and backgrounds therefore achieving a high scientific interaction which promotes learning and the spread of information. 
We also encourage communication in foreign languages due to the multi-culturality of our group.
  • This graph shows the performance of various approximations schemes. The so-called Euler scheme is the traditional method. The other methods are the ones proposed by our team. The higher the slope the more accurate the method is.