Abstract
This paper is based on covariance and expected return, building portfolio risk optimization model. Using Genetic Algorithm and Quadratic Programming, three securities portfolio Optimization model is resolved, and we find that Genetic Algorithm having priority for Restraint Conditions is not a linear model.
Highlights
The number of securities transactions is generally limited in the capital market
In order to adapt the need for capital market and practical operation, it is necessary to research portfolio decision problem under risk constraint
This paper attempts to use genetic algorithm to solve this problem, and in order to verify the reliability of this method, a function with quadratic programming in Matlab to calculate the results is used
Summary
1) Determine population size M, crossover probability pc, mutation probability pm, maximum evolution generation maxgen, the vector of upper and lower bounds. 2) Use real-code, each chromosome contains n gene loci which represent insecurities, the genevaluation represents the proportion in securities portfolio. 3) It is easy to know the following super geometry contains feasible set from the constraints. We need to use the third step to generate a new chromosome, if the chromosome is feasible, we can accept it as a member of population, we use the notation x j , j = 1, 2, , M to denote M feasible chromosome after finite sampling. It is better to reorder the v j (0) according to the target value, and denote the first row chromosome as v0. If we find a better chromosome in the future evolution, use this and replace v0.
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