Application on the portfolio optimization problem of statistical mechanical informatics

近年来，在投资组合优化问题中，基于统计力学信息学的分析方法引起了众多跨学科领域研究者的关注。在以往的工作中，最小投资风险的情况下，每种资产的收益率是独立和相同的分布的典型行为进行了充分的研究，然而，最小投资风险的情况下，收益率是相互相关的是不够的。因此，我们研究的投资组合优化问题的相关情况下，使用三种方法，副本分析，适应Thouless-Anderson-Palmer方程和随机矩阵积分。此外，这些分析技术进行了改进，以处理相关结构。

Recently in portfolio optimization problem, the analysis based on statistical mechanical informatics attracts attention of a lot of researchers in cross-disciplinary fields. In previous works, the typical behavior of minimal investment risk in the case that return rate of each asset is independently and identically distributed is investigated sufficiently, however, the minimal investment risk in the case that return rates are correlated with one another is not enough. Thus we investigate portfolio optimization problem in the correlated case using three approaches, replica analysis, adapted Thouless-Anderson-Palmer equation and random matrix integral. Furthermore, these analysis techniques are improved in order to treat correlation structure.