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.There would be a term in the objective function involving the product of each pair of stock prices.The covariance of that pair of prices is also used in the objective function.A product renders the objective function a quadratic.There would of course be some linear terms as well, and they represent the individual stock prices with the stock’s average return as coefficient in each such term.You already get the idea that this optimization problem falls into the category of quadratic programming problems, which result in real number values for the variables in the optimal solution.Some other terms would also be included in the objective function to make sure that the constraints of the problem are satisfied.A practical consideration is that a real number value for the amount of a stock may be unrealistic, as fractional numbers of stocks may not be purchased.It makes more sense to ask that the variables be taking 0 or 1 only.The implication then is that either you buy a stock, in which case you include it in the portfolio, or you do not buy at all.This is what is usually called a zero-one programming problem.You also identify it as a combinatorial problem.You already saw a combinatorial optimization problem in the traveling salesperson problem.The constraints were incorporated into special terms in the objective function, so that the only function to be computed is the objective function.Deeming the objective function as giving the energy of a network in a given state, the simulated annealing paradigm and the Hopfield network can be used to solve the problem.You then have a neural network in which each neuron represents a stock, and the size of the layer is determined by the number of stocks in the pool from which you want to build your stock portfolio.The paradigm suggested here strives to minimize the energy of the machine.The objective function needs therefore to be stated for minimization to get the best portfolio possible.PreviousTable of ContentsNext | | Use of this site is subject to certain ,All rights reserved.Reproduction whole or in part in any form or medium without express written permision of EarthWeb is prohibited
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