Second-order Differential Algorithm And Its Application In Portfolio

Multi-objective optimization problem exists widely in engineering practice and scientific research,such as electronic and electrical engineering,mechanical design and manufacturing,communication and network,finance and other fields often meet the optimization problem that requires multi-objective modeling.Multi-objective evolutionary optimization algorithm(MOEA)has become one of the main emerging research fields,among which swarm intelligence algorithm is widely used and plays an important role.The difference algorithm is easy to use and efficient in single objective optimization,and has been applied to a variety of MOEA and achieved good performance.The second-order difference algorithm is a single-objective optimization algorithm based on the traditional difference algorithm.Its second-order difference strategy has been verified to be superior to the traditional first-order difference in convergence and stability.It is worth studying to improve the performance of second order difference algorithm by using multi-objective optimization.In this paper,the difference and second-order difference are introduced in detail,and the multi-objective optimization algorithm and related concepts are also described in detail.Finally,it is used as an operator to replace the original mutation and crossover operator,and is fused with the multi-objective framework based on decomposition to obtain the multiobjective second-order difference algorithm MOEA/D-SODE.The performance of MOEA/D-DE algorithm is compared with that of MOEA/D-DE algorithm based on difference strategy.Numerical results show that MOEA/D-SODE has stronger convergence and distribution than MOEA/D-DE.Portfolio optimization is the process of determining investment proportion portfolio based on risk,which aims to reduce risk and gain more profit in investment.Using covariance as a risk measure,the birth of mean-variance portfolio optimization model has brought a revolutionary approach to quantitative finance.As computing power and algorithms have improved,a great deal of effort has been made to improve the model.As a kind of financial derivatives,option is an effective risk hedging tool.Scholars have made great achievements in the research of security investment which uses financial derivatives to hedge investment risks.This paper first introduces the mean-variance model,and then proposes a multi-objective portfolio model with options.Firstly,fuzzy mathematics and uncertainty theory are used to model stock and option investment respectively,and the return rate of investment is calculated.Fuzzy variance and information entropy are used as the other two objectives to model the single-stage and multi-stage portfolios respectively.The real data of Shanghai-Shenzhen 300ETF are used for empirical analysis,and the multi-objective second-order difference algorithm with constraint processing mechanism is used for optimization.The values and images show that Pareto solution set has a certain distribution,which also proves the performance of MOEA/d-sode in dealing with practical problems and the practicability of the model.The control experiment of single-stage model shows that option can still hedge the risk of stock investment and improve the return in multi-objective model.Joining fixed-income investments reduces risk;Increasing the upper limit of each asset investment ratio can expand the income range.The multi-stage and single-stage control experiments show that the multi-stage return rate is significantly higher and the solution set distribution is significantly better,which proves that the investment strategy is still effective in the multi-objective model.