This research project was selected on October 2009 by the Japan Science and Technology Agency (JST) as one of the projects in a research field "Alliance for Breakthrough Between Mathematics and Sciences (ABMS)" under the JST's basic research promotion programme "Core Research for Evolutional Science and Technology(CREST)". Our research team, led by Assoc. Prof. Dr. Arturo Kohatsu-Higa of Graduate School of Engineering Sciences in Osaka Univeristy, kicked off the research project on October 2009. This research project is undertaken under the management and operation by the Center for the Study of Finance and Insurance (CSFI), Osaka University and Ritsumeikan University's Research Center for Finance.