An application of Particle Swarm Optimization (PSO) on the optimal portfolio selection by goal programming

Abstract

Portfolio is the set of assets either real or financial owned by investor. One asset used by investor is stock because the stock has various price along the period time. Nowadays, stock investments have been done by investors. Stock price can be either profit or loss so that it is required portfolio selection. From the various price of stock, we can compute the return, expected return, and the risk of stock. In this research, we will make the optimal portfolio which can result maximum return and minimum risk of stock with the available investation. Goal programming is the mathematical programming techniques to solve the objectives subject to some constraints where the there are priorities for each objective. An application of goal programming is portfolio selection. Portfolio selection is determining some stocks optimizing maximum return and minimum risk of stock with the available investation. The novelty of this research is Goal Programming as portfolio selection method will be optimized by Particle Swarm Optimization (PSO) so that it is called Particle Swarm Optimization-Goal Programming (PSOGP). In PSO, there is initialization of particle i.e. proportion of investation on each stock as decision variable. Particle must be constructed so that it can satisfy the constraint investation of all stocks. In optimization process, the new particle is also modified so that satisfying the constraints. In multiobjective optimization, sort the fitness on the value of the first priority objective. If first fitness have the same value of the objective, then sort them on the second priority objective, and so forth. Based on simulation, PSOGP can be applied on the portfolio selection and can optimize priority of some objectives.