The Optimal Portfolio And Limit Theorem With Transaction Costs

The major problem facing investors has always been the maximizationof wealth in a world of uncertainty. Portfolio selection is how to allocatewealth among alternative assets of a basket. The mean-variance approach byMarkowitz provides a fundamental basis for portfolio construction in a singleperiod. The most important contribution of this model is that it quanti?es therisk by using the variance, which enables invertors to seek the highest returnafter specifying their acceptable risk level. E?orts in extending, the core of the Markowitz mean-variance model is totake the expected return of a portfolio as the investment return and the vari-ance of expected returns of a portfolio as the investment risk. Due to changein the expectation of the future returns of securities, most of the applicationsof portfolio optimization involve the revision of an existing portfolio. Therehave been numerous e?orts to illuminate the role of transaction costs portfoliomanagement, much of the work having been focused on Merton's problem. This thesis focuses on there existence condition of the optimal solution ofwhich convex programming model of portfolio select and it's limit of portfolioselection problem with transaction costs based on generalization risk function,and discussed the continuous-time portfolio selection with consumption understochastic linear-quadratic framework. The organization is as follows. The ?rst chapter, we construct a combination predictive model of timeseries markov chain, which has been tested on real data from the ShanghaiStock Market. Using several ?tting predict methods in the empirical analysis. The second chapter, a convex programming model with respect portfolioselect with transaction costs in single period was present, then we provedthe optimal solution's existence condition and the equivalence of this model.Finally, we illustrate a special example for the optimal solution. viii新疆大学博士学位论文 徐云 The third chapter, we discuss the relationship between the limitation of theoptimal solution sequence and corresponding expectation of relate return se-quence of portfolio in multiperiod, prove the limit Theorem of above sequences. In fourth chapter, the limit Theorem of optimal portfolio in multiperiodwith information was present. Then given the economic interpret of somecases. The last chapter concerned with a continuous-time portfolio selection modelon optimal control. The objective is to minimize the variance of the termi-nal wealth for a given expectation return level. We obtain the optimal so-lution of the original problem located via the solution of a stochastic linear-quadratic(LQ).