Studies on Adaptive Portfolio and its Eguilibrium Price

研究了均方误差跟踪下的多目标自适应指数基金投资决策问题。我们的投资问题考虑了期望收益最大化和风险最小化这两个相互矛盾的多目标函数。利用目标规划技术推导出最优决策，并将结果发表在学术期刊上。另一方面，在均方跟踪误差准则下，利用贝叶斯方法设计了自适应指数基金。我们将注意力集中在具有已知方差-协方差矩阵的未知收益率向量上。研究表明，利用前沿投资组合之间的简单关系，建立了一种适应性调整方法。这些结果已在日本运筹学学会的研讨会上以及在新西兰和美国举行的国际会议上得到了报道。此外，一些研究成果还发表在学术期刊上，并征求了研究人员的意见和反映。适应性投资组合的均衡价格以及个体证券与投资组合之间的关系等问题有待于进一步研究。

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.