Study On Particle Swarm Optimization Algorithm And Its Application In Portfolio Optimization

The main content of this paper is analyzing and researching the particle swarm optimization and its algorithmic improvement, and applying it in the portfolio.The proposition are proved as liable and efficient methods to solve the multi-factor optimal model for portfolio. The new algorithm puts out in this paper has faster convergence speed and much more precise solutions.The particle swarm optimization (PSO) algorithm is a kind of efficient method to solve optimal problem in a group of algorithm that are called swarm intellegence. The PSO algorithm is a kind of searching method which simulates the food searching of birds in natural world. It has been used in broad fields,The modern portfolio theory puts forward the ideology and method that the least variance used to make portfolio, and uses statistical technology to analyse the affection of expectational yield and risk that resulted by portfolio. And it also brings forward the method that invest with the selective conformation of efficient portfolio of preference on yield and risk.This paper sets out from application angle, establishes the multi-factor optimal model for portfolio in the condition of considering real factors in the market, the bank saving investment factor has also been considered. So the model becomes more suitable for the problem. Preference coefficient in the model is used to enhance the investor's flexibility of stocks choosing.The PSO algorithm is a kind of simple and robust algorithm , and easy to implement, especially doesn't need the special field knowledge,and only uses fitness function as an assessment to instruct the search process. Now the PSO algorithm has got a lot of fruits in diferent application fields, and arose many scholars' attention. The PSO's speciality makes it possible to apply PSO algorithm in the field of portfolio.But the basic PSO algorithm has some disadvantages such as bad performance on convergence in afternoon time and easy getting in local extremum and bad performance on precision. Sometimes, algorithmic improvement is needed when put into practical fields.This papert studies the PSO algorithm meticulously, and make some improvement to the basic algorithm base on the practical problems. A new kinf of PSO algorithm : solution space shrinking PSO(sssPSO) is introduced. This is a efficient and general PSO algorithm.The creative factor in solution space shrinking PSO is the solution space shrinking theory , which based on the idiosyncrasy of approachability in basic PSO algorithm, and having the same performance with iterative expressions. The sssPSO also has the function of precision control.Then, when establish the material solution space shrinkage strategy, a mathod of proportional shrinkage is established. And the combination of solution space shrinking and iterative approaching is used. And the balance of inner iteration times and shrinkage coefficient is set carefully. The new algorithm has a excellence performance , especially on convergence in afternoon time and precision.The solution space shrinkage happens when basic PSO is used for certain times, then after shrinking, new generational particles created and initialized, and then basic PSO going on. This procedure can be expressed as a recursive procedure.Fundamental process of sssPSO:Step 1 set initial solution space, randomly initialize m particles in the solution space demarcated by vectors X_low and X_up, use basic PSO to iterate a certain times marked by variable C_in ,then return the best particle PStep 2 check that whether the difference of X_low and X_up is small enough, if so , exit the algorithm with Pi of P as the solution, if not,continue Step 3 shear the solution space of Pi of P with the shrinkage coefficient k, and get a new pair of demarcative vectors X_low and X_upStep 4 randomly initialize m particles in the solution space demarcated by vectors X_low and X_up, use basic PSO to iterate a certain times marked by variable C_in ,then return the best particle P, goto Step 2 According to the special requirement of multi-factor optimal model forportfolio, the arithmetic sum of each dimension of every particle must equal to 1,algorithmic improvement is needed for sssPSO, so a modified sssPSO is put forward by redefining the iterative expressions, then the solution can be feasible.Fundamental process of modified sssPSO:Step 1 randomly initialize m particles in the solution space demarcated in [0,1], for each particle, make proportional transform to each dimension, make the arithmetic sum of each dimension equaled to 1Step 2 use modified basic PSO(using iterative expressions 5.1 and 5.2) to iterate a certain times marked by variable C_in , then return the best particle PStep 3 check whether the difference of X_low and X_up is small enough, if so , exit the algorithm with Pi of P as the solution, if not,continueStep 4 shear the solution space of Pi of P with the shrinkage coefficient k, and get a new pair of demarcative vectors X_low and X_upStep 5 randomly initialize m particles in the solution space demarcated by vectors X_low and X_up, for each particle, check whether the sum of fist n dimensions is no more than 1, if so, the value of the last dimension of the particle is equaled to the difference of 1 and the sum, if not goto Step 5Step 6 use modified basic PSO to iterate for a certain times that marked by variable C_in ,then return the best particle P, goto Step 3Then put these strategies to solve the multi-factor optimal model for portfolio, eclipse 3.3 environment is used to proved the efficiency and performance of the new mathods. The data are collected from real stock market. Thought practical numerical calculation, better result is obtained, proving the validity and feasibility of sssPSO.Compared with basic PSO algorithm, the new algorithm has faster convergence speed and much more precise solutions, which accord with the academic conclusion.