Studies on Adaptive Portfolio and its Eguilibrium Price

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This study is concerned with an investment decision problem with multiple criteria and an adaptive index fund under mean square error tracking. Our investment problem considers the multiple objective function like maximization of the expected return and minimization of risk which is contradictory to each other. The optimal decision is derived by goal programming technique and the result is published in the academic journal. On the other hand, the adaptive index fund is designed by a Bayesian approach under the mean square tracking error criterion. We have concentrated on our attention to an unknown rate of return vector with the known variance-covariance matrix. It has been demonstrated that an adaptive readjustment method is established by mean of a simple relationship between frontier portfolios.These results were reported in the workshop in the OR society of Japan and in the international conferences held in New Zealand and U.S.A. In addition, some of them are published in the academic journals and the comments and reflects from researchers have been required. Many problems of the equilibrium price of the adaptive portfolio and of the relationship between the individual security and the portfolio are left for future research.