The Mean-Variance Portfolio Problem Under The Non-extensive Model With Jumps

Portfolio selection plays a significant role in modern financial research.Mean-variance portfolio theory is the core research content of the portfolio theory.In this paper,we study the non-extensive financial market model with jumps of mean-variance portfolio selection problem.The research on this issue not only perfects the port-folio theory,but also provides practical methods for investors in securities market to solve the problem of investment options.Firstly,we establish a non-extensive financial market model with jumps,which effec-tively depicts the price process of financial assets,and describes the asset prices with the character of peak and fat tail.Secondly,the author studies the mean-variance investment selection problem under the market model,and further studies the two cases of short selling and no short selling respectively.On the basis of the research,we get the analytic solution of the optimal investment strategy for two cases,as well as the corresponding mean-variance efficient frontier.Then the paper discusses the parameter estimation problem of non-extensive model with jumps.According to the identification method of jumps,the paper firstly gives the estimation of the jump parameters.We obtain the non-extensive distribution parameters estimation by the maximum likelihood estimation through the discretization of the model.Finally,we apply the research results into China’ s financial market.By establishing the nonextensive distribution model with jumps for Shanghai Stock Index,we obtain the corresponding parameter estimation and apply it to the mean-variance portfolio selection problem.So that the research gets the optimal portfolio solutions,and compares the effects of various parameters on the investment strategy.