Effective solution of a portfolio selection based on a block of shares by a meta-controlled boltzmann machine

Abstract

In a real investment, stocks are dealt with based on a block of shares. A block of shares is a minimum unit for trading stocks. However, a conventional portfolio selection problem does not consider about a block of shares. If we deal with stocks according to a block of shares, real allocations of funds to each stock should differ among the cases of different amounts of money. Furthermore, a decision maker should be unable to buy less than one block even if the investing ratio for some stock is much smaller. The objective of this paper is to build a portfolio selection model in consideration of the amount of investing funds and a block of shares. Our model is formulated as an integer quadratic programming problem. In general, an integer nonlinear programming problem is difficult to solve for all but the smallest cases. So we also propose the efficiently approximate model employing a Meta-controlled Boltzmann machine. © Springer-Verlag 2004.