# Hierarchical decision making in strategic investment by a Boltzmann machine

Teruyuki Watanabe, Junzo Watada, Kenji Oda

Research output: Contribution to journalArticle

8 Citations (Scopus)

### Abstract

A conventional portfolio selection problem, which is based on a mean-variance model, is difficult to solve by using mathematical programming techniques. This difficulty is caused by the fact that the corresponding mathematical programming problems are large-dimensional one, since almost all variance-covariances of return rates are, typically, not zeros. In this paper, we propose an efficient method for solving a portfolio selection problem, a method which uses a Boltzmann machine. In a real-life problem, it is also important to find the optimal combination of a small number of invested securities out of many securities in a market, because of a limited amount of funds to invest into securities. So we also propose a portfolio selection method to obtain the invest ratio of limited number of securities out of huge number of securities using a multi-stage application of the Boltzmann machine.

Original language English 429-437 9 International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems 7 4 Published - 1999 Aug Yes

### Fingerprint

Mathematical programming
Decision making

### Keywords

• Boltzmann Machine
• Index Data
• Limited Number of Securities
• Multi-Stage Model
• Portfolio Selection Problem

### ASJC Scopus subject areas

• Artificial Intelligence
• Control and Systems Engineering

### Cite this

Hierarchical decision making in strategic investment by a Boltzmann machine. / Watanabe, Teruyuki; Watada, Junzo; Oda, Kenji.

In: International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, Vol. 7, No. 4, 08.1999, p. 429-437.

Research output: Contribution to journalArticle

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