Extreme value models for multi-variate data and its application to risk management

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We investigated statistical methods for modeling and analyzing extremal co-movements of multivariate data and their applications to the measurement of the imapact of extremal events and risk management in fiance and related fields. The results indicate that the regime switching model is very useful both from theoretical and practical view points for it flexibly represents such structural changes of multivariate data as error covariances according to state changes of a latent variable. In some applications to financial markets, regime switching models identify high risk and low risk regimes and suggest appropriate investment opportunities and risk management depending on the current regime as well as future regime forecast.