Measuring Financial Risks

本项目的主要目的是重新审视计量经济学分析和金融工程文献中常用的衡量金融风险的统计方法。首先，我们探讨了金融风险分析和未定权益价格评估的主要概率方法。它们是基于随机过程理论，特别是基于连续扩散过程和半鞅过程的理论，我们研究了它们的应用，包括未定权益估价方法。特别是，我们发展了一种新的渐近展开方法来评估利率为随机的复杂未定权益，这是数学金融学中一种很有前途的未定权益评估的新方法。此外，我们还研究了金融问题的半鞅方法，并考察了现有的信用风险定价方法。当金融市场存在一定的违约风险时，就可以进行…其次，研究了度量金融风险的统计方法，包括统计时间序列分析和统计生存分析(统计可靠性理论)。特别是，我们研究了统计分析中相关系数的扩展Copulas和用于研究包括利率风险在内的金融风险的状态空间建模。第三，在本项目的研究工作下，在金融风险度量方面取得了许多新的结果。我们的研究项目的详细结果已在国内和国际学术会议上报告，并已经(或将会)在本报告列出的学术论文中报告。总而言之，我们实现了该项目最重要的目标。参与这一项目的6名成员有效地撰写了许多论文，也激励了大量相关领域的研究人员和国际学术界的一些统计学家。我们感谢文部科学省和日本科学促进会对我们研究项目的慷慨支持。较少

The main purpose of this project was to re-examine the existing statistical methods often used in measuring financial risks in econometric analysis and financial engineering literatures.First we have inverstigated the major probabilistic methods for analyzing financial risks and evaluation of contingent claim prices. They are based on the theory of stochastic processes, the continuous diffusion processes and the semi-martingale processes in particular, and we have investigated their applications including contingent claim valuation methods. In particular we have developed the new asymptotic expansion approach for evaluating complicated contingent claims when the interest rates are stochastic, which is a promising new approach to the contingent claims evaluations in mathematical finance. Also we have investigated the semi-martingale approach to financial problems and examined the existing pricing methods of credit risks. When there are some default risks in the financial market, it coul … More d be incomplete and we have examined the mathematical finance theories of related problems in the incomplete financial market.Second, we have investigated the statistical methods for measuring financial risks including the statistical time series analysis and statistical survival analysis (statistical reliability theory). In particular we have investigated the copulas which is an extension of the correlation coefficient in stattistical analysis and the state space modeling for investigating the financial risks including the interest rates risks.Third, there have been many new results we have obtained under the research efforts of this project on the financial risk measurements. The details of the results under our research project have been reported in domestic as well as international academic meetings and have been (or will be) reported in academic papers listed in this report.In conclusion, we have acomplished the most important objectives of this project. Six members participated in this projectofficially have written many papers and also stimulated a large number of researchers in the related fields and some statisticians in the academic international perspectives We thank The Ministry of Education, Science, Sports and Culture and Japan Society for the Promotion of Science for giving the generous support to our research project. Less