Theoretical Research on the problem of dynamic portfolio selection based on new approaches and Its Application

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Miura Ryozo: He has been working on Theoretical and empirical study on portfolios which utilize rank information. He is still on the stage of empirical study on size effect stochastic process of stocks, which is most essential in order to study the nature of the rank portfolio. Along with this study, he took a different look at the rank of stock prices which is not the rank of a stock among many stocks, but the rank of the price of a stock at a prefixed time among the prices of the same stock during a prefixed time interval. He has studied and derived a probability distribution of this rank of a price of a stock. Then he utilized this result for pricing of a new exotic option, named Stochastic Corridor Option, which he created during this research project.Nobuhiro Nakamura: We study several issues involving optimal risk transfer associated with a new security innovation from its issuer to investors based upon a stochastic differential utility (SDU). Using the stochastic maximum principle we have shown that the optimal risk transfer, consumptions, investment policies of both agents are characterized by a forward-backward stochastic differential equation system. Furthermore we have explored the SDU-based maximization problems with an uncertain time horizon, event risk and model risk.Izumi Nagayama: She has tested numerically for the effectiveness of model-risk-hedging based on the Black-Scholes model. She found out that the well-known vega-hedging does not always work well and she also examined the reason. She is trying to find the new way of hedging the model risk.Shoji Kamimura: Recently, Fujita and Miura(2006) have provided mathematical closed forms for the probability distribution of the rank. However, these closed forms are so complicated that we can not see or imagine the figure shape of the probability distribution. Then we have shown some numerical results to see the figures and properties of these family of distributions of the rank statistics.