The Application Of Some Optimization Algorithms In The Portfolio Models

With the development of optimization algorithms, a lot of researchers have adopted them to solve many kinds of optimization problems in real life. When the modern portfolio theory develops up to now, there are many excellent researches at home and abroad. This paper’s main study is the applications of optimization algorithms in the portfolio models. The models in the paper contain investors’risk preference parameters. It can reflect investors’risk preference well. The main contents and results are summarized as follows:(1) Build three indexes. The first one is residual income-variance ratio. It can be used to choose excellent security. The second one is deviation portfolio of portfolio model which can be used to evaluate portfolio selection models. At last, on the basis of the variance and the second half of the variance, this paper puts forward a new risk measure-combination half variance.(2) This paper introduces the applications of rotation algorithm, particle swarm optimization algorithm, a new modified hybrid conjugate gradient algorithm and non-smooth unconstrained algorithm in the portfolio models. The paper proves the new hybrid conjugate gradient algorithm and its modified algorithm’s descent property, global convergence, and also provides numerical test.(3) When not allowed short selling, use rotation algorithm and particle swarm optimization to solve the portfolio models with different constraint conditions. Portfolio models allowed short selling only contain one equality constraint. Among them, use to transform the constrained optimization problem into unconstrained optimization problem. Use modified hybrid conjugate gradient algorithm and non-smooth unconstrained algorithm to solve portfolio models with U-transaction cost function and V-transaction cost function.